When transporting cellular cargoes along the cytoskeletal filament track, motor proteins produce additional frictional drag. This "protein friction"determines the mean speed of a cargo for a given force and the energy dissipated per chemical cycle. Motor protein friction has been measured directly in an optical tweezer experiment, and can also be estimated from the force-velocity curve, close to stall. We present a mathematical and computational study of this phenomenon. In our model, a motor protein is elastically linked to a μm-sized cargo particle, and undergoes tightly coupled, biased random walk-like motion on the microtubule filament, the bias being contributed by nucleotide hydrolysis as well as stretching of the linker "spring", with spring constant κ. The cytoplasm is assumed to be a Newtonian fluid, which exerts a damping force γ V on the cargo moving with velocity V. The effective drag coefficient γeff = F/V is measured in our numerical simulations, where F is the net external force on the cargo, including motor-induced force, near F = 0. The motor friction γm = γeff- γ is predicted theoretically and compared with simulation data for a range of values of κ and γ. The predicted values for small γ are found to be similar to experimental results, though smaller in magnitude. Numerical simulations also show that γm is a weakly increasing function of γ, and is additive when multiple motors are involved in transportation. © 2021 EPLA.