Numerical simulations of triaxial compression tests are performed in order to investigate the applicability of the material point method (MPM) to large-deformation geotechnical problems. A Mohr-Coulomb constitutive model is adopted as a geotechnical nonlinearity, for which parameters are obtained by experimental results. The stress-strain relationships obtained in the simulations show good agreement with the experiments at high levels of strain, thus demonstrating the effectiveness of MPM. Parametric studies are also performed in order to investigate factors that influence the relationship between the initial and final shear bands observed during simulations of triaxial compression tests. The main findings of the study are followings: (1) initial shear bands are generated near the constrained edges of a specimen; (2) when both top and bottom edges of a specimen are constrained, initial shear bands near the edges at which the external forces are applied develop finally into clear shear bands; (3) specimen geometry has a major influence on the formation of shear bands in the case of rectangular specimens.