Glaciers calving ice into the ocean is predicted to significantly contribute to sea-level rise and will thus influence future climate. Although numerous factors that induce glacier calving have been identified and studied, it is still extremely challenging to develop a unified and continuum computational framework that simulates ice fracture and glacier calving taking into account all important ingredients such as the interaction between ice and water, including buoyancy and melting, on complex and large scale geometry. This prevents scientists to precisely predict calving rates at the outlet of glaciers. Here, we propose to address this issue through numerical simulations of glacier calving based on the Material Point Method and finite strain elastoplasticity. A non-associative Cam-Clay model was developed to simulate the ice while the water is modeled as a nearly in-compressible fluid. First, simplified 2D simulations were performed to analyse the size of calved icebergs which were in good agreement with analytical solutions. The model reproduces not only the vertical glacier fracture observed in real calving events but also iceberg formation and tsunami-wave generation. Finally, 3D simulations of glacier calving were performed, taking into account opened crevasses on the top of the glacier. Although at a preliminary stage, and lacking experimental validation, we show the promise of our approach for modeling glacier calving, and more generally glacier and sea-ice dynamics.