A systematic ab initio study within the density functional theory is employed to investigate the structural, mechanical, elasto-acoustic, and anisotropic properties of AePdH3 (Ae = Ca, Sr, Ba) perovskites. A close agreement is found, while comparing the calculated ground state structural parameters with available results. The estimated results of formation and cohesive energy indicate that the presented hydrides are energetically stable and synthesizable. The pressure induced elastic stiffness constants revealed that the studied hydrides are mechanically stable with satisfying the Born stability criteria. The pressurized mechanical properties are evaluated in estimating the elastic constants by the stress-strain method formulating the Voigt-Reuss-Hill approximation. In view of Poisson's ratio, Pugh's ratio, and Cauchy pressure, all perovskites behave as ductile and soft manner. Utilizing elastic moduli, Debye temperatures along with isotropic acoustic velocities as a function of pressure are discussed in depth. The anisotropy is explained by means of elastic anisotropy factors, three-dimensional (3D) elastic moduli, acoustic sound velocities, and minimum thermal conductivities. According to all indexes, all perovskites are exhibited anisotropic nature except 3D contour plots of linear compressions, isotropic instead, and the maximum anisotropy is achieved in BaPdH3 hydrides.