Methods for modeling crustal deformation related to earthquakes and plate motions have been developed to incorporate complex crustal structures and multi-fidelity observations. A machine learning approach called physics-informed neural networks (PINNs), which can solve both forward and inverse problems of physical systems, was proposed and applied to the forward simulations of antiplane deformation. Here, we aimed to extend the PINN approach to crustal deformation in two directions: (1) inplane deformation, which is typically used for modeling subduction zones, and (2) inversion analysis of fault slips from geodetic observations. We verified the performance of PINNs on these problems and suggested that formulations in Cartesian and polar coordinates are suitable for forward and inverse modeling, respectively. Furthermore, PINNs yielded stable inversion results without explicit regularization terms, implying that solving the governing equations with PINNs implicitly imposes regularization based on the physical requirements. This may elucidate the distinctive properties of PINNs and provide insights into inversion analyses in geophysics and other fields.