Modeling of coupled plastic flows and strain-induced phase transformations (PTs) under high pressure in a diamond anvil cell is performed with the focus on the effect of the contact sliding between sample and anvils. Finite element software ABAQUS is utilized and a combination of Coulomb friction and plastic friction is considered. Results are obtained for PTs to weaker, equal-strength, and stronger high pressure phases, using different scaling parameters in a strain-controlled kinetic equation, and with various friction coefficients. Compared to the model with cohesion, artificial shear banding near the constant surface is eliminated. Sliding and the reduction in friction coefficient intensify radial plastic flow in the entire sample (excluding a narrow region near the contact surface) and a reduction in thickness. A reduction in the frictioncoefficient to 0.1 intensifies sliding and increases pressure in the central region. Increases in both plastic strain and pressure lead to intensification of strain-induced PT. The effect of self-locking of sliding is revealed. Multiple experimental phenomena are reproduced and interpreted. Thus, plastic flow and PT can be controlled by controlling friction.