Density functional-based method has been used to investigate the systematic trends for structural parameters, elastic stiffness, lattice dynamics and thermal properties of cubic perovskite-type RBRh3 depending on the type of R atoms (R are Sc, Y, La and Lu). The structural parameters, single-crystal elastic constants, directional elastic wave velocities and their pressure dependence are calculated and analyzed in comparison with the available experimental and theoretical data. A set of isotropic elastic parameters and related properties, namely bulk and shear moduli, Young's modulus, Poisson's ratio, Lame's coefficients, average sound velocity. Debye temperature and thermal conductivity are predicted in the frame work of the Voigt-Reuss-Hill approximation for the polycrystalline RBRh3. The correlation between the mechanical properties and electronic structures has been discussed. Using the density-functional perturbation theory (DFPT), the phonon properties of RBRh3 (R = Sc, Y and La) are investigated for the first time. (C) 2011 Elsevier B.V. All rights reserved.