The Dutch infrastructure counts many bridges, the majority of which are built in concrete. These bridges have been designed and constructed according to safety codes. A lot of these bridges date from the previous century and have been designed conform outdated safety codes. Therefore, the main problem of these bridges is the uncertainty with regard to their structural health as well as their performance under the current loading conditions. The application of ‘smart aggregates’ could potentially solve these issues. Smart aggregates refer to a network of sensors that emit and receive wave signals inside the concrete structure. These sensor are embedded within the concrete and can be implemented in both new and existing structures. The changes in the medium with regard to the stresses are reflected by the phase changes of the wave signal measured by the smart aggregates. This information allows for the monitoring of the conditions of the bridge during its lifespan. The magnitude of the stress in certain parts of the structure could then indicate the need for maintenance at an early stage, thus preventing unnecessary maintenance while preserving the safety of the bridge. This method, however, requires a thorough understanding of the wave propagation inside a concrete medium subjected to a stress state. This thesis investigates how the relative wave-velocity change of a concrete-like medium is influenced by the stresses to which it is subjected. Throughout the report this relation is referred to as the acoustoelastic effect. The first part of the thesis is centered around the theoretical formulation of the acoustoelastic effect. During this study, the models of Murnaghan and Biot have been studied. Subsequently, their differences with respect to the fundamental assumptions have been indicated. Here, it has been found that the main difference between the two models is demonstrated by the way they regard the second-order deformation terms. Murnaghan assumed that these terms are significant and has included them in the constitutive relation. From the latter, Hughes and Kelly have derived expression for wave velocities of a stressed medium, which have been verified with experimental results. On the other hand, Biot adopted the theory of infinitesimal deformations which omits the second-order deformation terms. In addition he based his theory around the wave propagation of a bending rod and extended this model to a three-dimensional medium subjected to initial stresses. This generalisation of an approximated model has led to analytical expressions for the wave velocity of a stressed solid which are contradicted by experiments. From this comparison, it has been concluded that Murnaghan’s model results in the most accurate representation of the acoustoelastic effect. The second part of the thesis focuses on the verification of the theoretical acoustoelastic effect through experimental research. For the purpose of verifying the acoustoelastic effect as well as determining the third-order elastic coefficients of a concrete-like medium, four specimens have been tested. In order to investigate the influence of the inhomogeneity of the material on the changes in the wave velocity, two different material compositions have been investigated. The first type consists of a homogeneous cement paste, whereas the second type represents heterogeneous concrete including aggregates. During the experiment, the different waveforms have been repeatedly emitted through a specimen subjected to an uniaxial compression. The relative wave-velocity change has then been obtained by post-processing the acquired data, which has been compared with Murnaghan’s model. The conclusion of this research is that Murnaghan’s theory can be used to accurately predict the relative wave-velocity changes of the cement-paste specimens, and in particular the relative P-wave velocity changes. The results have shown that the radial recordings yield inconsistencies which can be attributed to the small dimensions of the specimens. Furthermore, the influence of the inhomogeneity of the material on the relative wave-velocity changes manifests itself through a discrepancy in the acoustoelasticity. Here, it is found that the ratio between the aggregate size, the specimen dimensions and the wavelength of the signal determines the sensitivity to the acoustoelastic effect. Therefore, before the data from the smart aggregates embedded in a real structure can be interpreted, the experiments need to be improved and expanded. It is important to investigate the acoustoelasticity of waves with non-orthogonal propagation and particle-oscillation direction, while applying various stress states to the medium. This is because the smart aggregates are arranged in a network, where the signals are emitted signals are propagating through the structure via arbitrary paths between various transducers.