The large-strain problem on phase transformations (PTs) under compression in a diamond anvil cell is studied in detail using the finite-element method. The combined effect of transformation kinetics and ratios of the yield strengths of low- and high-pressure phases is examined. Some experimental phenomena (e.g., plateaus in pressure distribution and plasticflow to the center of a sample) are reproduced. Results are applied to interpretation of experimental data and characterization of strain-induced PTs.