Strain-induced phase transformations (PTs) under high-pressure differ fundamentally from the pressure-induced PTs under quasihydrostatic conditions. A model and finite-element approach to strain-induced PTs under compression and torsion of a sample in rotational diamond anvil cell are developed. The current paper is devoted to the numerical study of strain-induced PTs under compression in traditional diamond anvils while the accompanying paper [ V. I. Levitas and O. M. Zarechnyy Phys. Rev. B 82 174124 (2010)] is concerned with compression and torsion in rotational anvils. Very heterogeneous fields of stress tensor, accumulated plastic strain, and concentration of the high-pressure phase are determined for three ratios of yield strengths of low-pressure and high-pressure phases. PT kinetics depends drastically on the yield strengths ratios. For a stronger high-pressure phase, an increase in strength during PT increases pressure and promotes PT, serving as a positive mechanochemical feedback; however, maximum pressure in a sample is much larger than required for PT. For a weaker high-pressure phase, strong strain and high-pressure phase localization and irregular stress fields are obtained. Various experimentally observed effects are reproduced and interpreted. Obtained results revealed difficulties in experimental characterization of strain-induced PTs and suggested some ways to overcome them.