Concrete is a composite construction material, which is composed primarily of coarse aggregates, sands and cement paste. The fracture processes in concrete are complicated, because of the multiscale and multiphase nature of the material. In the past decades, comprehensive effort has been put to study the cracks evolution in concrete, both experimentally and numerically. Among all the computational models dealing with concrete fracture, the lattice fracture model wins at several aspects, such as being able to capture detailed crack information, high computational efficiency and stability. The lattice fracture model also enables to investigate how the fracture properties of concrete depend on its material structure. This can be achieved by projecting the lattice network on top of the original material structure of concrete. In this thesis a parallel computing code is described, which is implemented for the lattice fracture model, in order to reduce the computational time and to enable the analysis on even larger lattice system. The fracture properties of cement paste, mortar and concrete are highly related in nature. In this thesis the lattice fracture model is coupled with the parameter-passing multiscale modeling scheme to study the relationship of the fracture processes in cement paste, mortar and concrete. A multiscale fracture modeling procedure is proposed and demonstrated. Three levels are defined, including micrometer scale for cement paste, millimeter scale for mortar and centimeter scale for concrete. The lattice fracture model is applied at each scale respectively. The inputs required at a certain scale are obtained by the simulation at a lower scale. At the lowest scale in question, the micrometer scale for cement paste, inputs are determined by laboratory experiments and/or nanoscale modeling from literature. Besides the multiscale lattice fracture model, another highlight in this thesis is the development of the Anm material model, which can simulate a material structure of concrete with realistic shape aggregates. Compared with classic concrete material models, the shape of aggregates is changed from spheres to irregular ones, which is closer to reality. The aggregate particle shape is represented by spherical harmonic expansion, where a set of spherical harmonic coefficients is used to describe the irregular shape. The take-and-place parking method is employed to put multiple particles together within a pre-defined empty container, which can be interpreted as the material structure of concrete. The key element in this parking algorithm is to check whether two particles overlap, as no overlap is allowed in the resulting simulated material structure. The multiscale lattice fracture model and the Anm material model, proposed and established in this thesis, can be used by researchers in concrete community, to study the various factors which influence the mechanical performance of cementitious materials. They can also be adapted with other computational models to form a complete fully multiscale modeling framework, from nanoscale to macroscale.