Recently, we studied, both experimentally and theoretically, the thermal and baric evolution of linear-in-field magnetoresistive (LMR) properties of the layered, compensated, and semimetallic CaAl₂Si₂.¹ One of our results indicates that the thermal and baric evolution of LMR curves manifest various transition/ crossover events (based on which a detailed P-T phase diagram was constructed). The origin of these transition/ crossover events is not clear, most probably due to structural or electronic phase transitions.² To gain more insight on these events, we carried out both theoretical and experimental investigation on the baric evolution of the crystalline and electronic structures of CaAl₂Si₂ and, for comparison, on all MAl₂Si₂ (M=Sr, Ba). Theoretically, while the calculated electronic structures (e.g. N_EF density of states at E_F ) do not manifest any anomalous feature, the ab initio calculations predict a monotonic reduction of the lattice parameters and, in addition, various structural phase transitions: e.g. P-3m1 to I4/mmm at P_c = 8 GPa for M=Ca, P-3m1 to I4/mmm at 5 GPa for M=Sr, and finally Pnma to I4/mmm at 4 GPa for M=Ba. We measured room-temperature pressure-dependent diffractograms up to 9 GPa. With no adjustable parameters, the baric evolution of lattice parameters confirms the corresponding theoretically calculated lattice parameters curves. Nevertheless, no phase transition is observed within the measured pressure range which was limited by the then available beamtime. We discuss the discrepancy regarding the predicted structural phase transitions.