Density functional theory is used to explore the physical properties of the new half-Heusler alloys XRhZ (X =V, Nb and Z = Si, Ge). The exchange-correlation effects were treated by the TB-mBJ potential. The four studied compounds are nonmagnetic semiconductor with an indirect band gap. The formation enthalpy, cohesive energy and phonon band structures demonstrated that these semiconductors are structurally and dynamically stable. It was predicted by the elastic study that the XRhZ compounds (X = V, Nb and Z = Si, Ge) have stable mechanical properties, they possess an anisotropic character and reveal the ductile nature with a B/G ratio >1.75. The optical results show an interesting photocatalytic potential for the NbRhSi and NbRhGe semiconductors; they exhibit a high absorption coefficient in the visible domain, which is around 112.104 cm-1. For energies greater than 10 eV (UV domain), the refractive index is less than one. The thermoelectric results confirmed that the XRhZ (X=V, Nb and Z=Si, Ge) compounds are very attractive for thermoelectric devices working in large temperature range including ambient temperature.