In recent years, machine learning methods have gained significant attention for solving partial differential equations (PDEs) [1]. Physics-Informed Neural Networks (PINNs) represent a class of unsupervised learning techniques in which shallow or deep neural networks approximate PDE solutions. The solution of a boundary value problem is formulated as an optimization task, where the loss function is designed to enforce the PDEs at collocation points within the domain of interest. An alternative to PINNs is the Variational Physics-Informed Neural Networks (VPINNs), which, instead of the PDE itself, utilize the variational formulation of the boundary value problem [2]. In this work, a VPINN framework is proposed and investigated to approximate solutions of solid mechanics problems using the weak formulation of the corresponding PDEs. The methodology is developed and implemented while exploring different test functions and numerical integration techniques. The advantages of VPINNs, including accuracy, flexibility, and computational efficiency are analyzed and demonstrated through numerical examples involving PDEs in solid mechanics.