Rare earth ternary borides, RRh3Bx (R = La, Gd, Lu and Sc) have been synthesized by arc melting method. Borides RRh 3Bx (R = La, Gd, Lu and Sc) have perovskite-type cubic structure: space group Pm3m; Z = 1. The lattice parameters a of the stoichiometric RRh3B for R = La, Gd, Lu and Sc are 0.4251(1), 0.4183(1), 0.4126(1) and 0.4080(1) nm, respectively. LaRh3B x does not have boron-nonstoichiometry as x = 0. In GdRh 3Bx and LuRh3Bx, boron- nonstoichiometry ranges between 0.55 ≦ x ≦ 1 and 0.30 ≦ x ≦ 1, respectively. The boron-nonstoichiometry range is the widest, 0 ≦ x ≦ 1, for R = Sc. Boron-nonstoichiometry increases with decreasing atomic radius of R. The microhardness of the stoichiometric RRh3B for R = La, Gd, Lu and Sc is 4.2 ± 0.1, 6.8 ± 0.1, 7.7 ± 0.5 and 9.9 ± 0.1 GPa, respectively. As a result, microhardness increases with decreasing atomic size of R in RRh3B; R is positioned at the eight corners of the cube in the perovskite-type structure. Thus, hardness is strongly dependent on R element. The hardness changes almost linearly with boron concentration x for R = Gd and Lu in RRh3Bx, while no linear dependency is found for R = Sc. Ab initio calculations have been performed to obtain the equilibrium lattice constants and the bulk moduli. The calculated lattice constants are in excellent agreement with experimental results. {\textcopyright} 2005 Elsevier B.V. All rights reserved.