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There is still a challenge to rapidly and accurately acquire the composition dependence of mechanical properties of multi-principal element alloys due to their huge composition space and complex electronic structures. Aiming to straightforwardly tune the mechanical properties through alloying, we systematically calculate the elastic and mechanical properties for four selected body-centered-cubic (bcc) Ti− Nb−M (M = Zr, Mo, Sn, Ta) refractory medium-entropy alloys (RMEAs) using a first-principles method. It is shown that the elastic stability of the bcc RMEAs can be significantly (weakly) improved with the increase in Nb, Mo, and Ta (Sn) content, but it is insensitive to Zr. The elastic stability, elastic modulus, hardness, and strength generally enhance, whereas Pugh's ratio and Zener anisotropy (A Z ) decrease with the increase in valence electron concentration. Additionally, there is a correlation between the magnitude of the A Z and the shape of the single-crystal Young's modulus (E [hkl] ). The largest (smallest) E [hkl] appears in the <111> (<100>) direction. Particularly, the most isotropic Ti 60 Nb 20 Mo 20 has the highest hardness and strength among all the Ti−Nb−M alloys. Moreover, the change of elastic properties induced by alloying is related to the change of density of states. This work sheds deep light on the design of high-performance Ti-based multi-principal element alloys.