The aim of this work was to study by means of the full potential linear muffin‐tin orbital method within generalized gradient approximation (GGA) and GGA + U approach the various physical properties of the NbCoSn and NbFeSb half‐Heusler compounds. The equilibrium ground states properties were calculated and compared with available experimental and theoretical data. The elastic constants have been calculated, and revealed that our compounds are mechanically stable. The obtained elastic modulus divulged that our compounds are elastically anisotropic and categorizing them as brittle compounds. The GGA approach showed a semi‐conductor nature. However, the GGA + U approach showed a significant improvement over other theoretical work. We remarked from the band structures that the two materials showed a p‐type semiconductor, with relatively high power factors. Furthermore, the optical quantities are calculated and discussed in detail. Hence, by our findings, the studied compounds could be used for thermoelectric and optoelectronic applications.