High-fidelity models in computational mechanics, applied in structural engineering and material research, are developed to be accurate, detailed and robust. These models enable new ways of research, such as developing highly-tailored microstructures in materials. To bypass excessive computational times needed to execute these models, Reduced Order Models (ROMs) can be implemented, which reduce the dimensionality of a problem by projecting it onto a reduced-order latent space. While projection-based ROM usually makes use of Proper Orthogonal Decomposition (POD) to obtain a linear basis needed for Galerkin projections, this thesis describes the development of a Variational Autoencoder-based (VAE) approach, which allows for learning a nonlinear latent space. POD-based and a VAE-based techniques are developed and applied for a case study of a simply supported beam, loaded into plasticity by a single movable point load. The ROM results are compared to the Full Order Model (FOM) results. Results are analysed and compared between the POD- and VAE-based techniques, and for different (hyper)parameters within the VAE-ROM results. The results show the VAE-based ROM outperforms POD-counterparts, especially in extrapolation and with the condition that a large enough dataset was used for training the VAE. Of the analysed parameters used for training the VAEs, the influence of dataset size and latent space dimensionality is observed to be significant, while the degree of regularization in the VAE and the activation function are of limited influence. Furthermore, this study shows that the validation loss of a VAE during training is not a good indicator for the performance of the VAE-based ROM, and suggests to consider the VAE-ROM error already during training of the VAE.