Growth theory of III-V nanowires fabricated by molecular beam epitaxy is developed to reveal the role of the substrate which can be either unpatterned or masked with an inert SiOx, layer. Axial and radial growths of nanowires are described in both cases, converging to the asymptotic stage which is independent of the substrate due to the shadowing effect. The nanowire lengths and radii are calculated as functions of time and the growth parameters. Good fits are obtained with the data on the growth kinetics of GaAs, GaP, InAs and InP nanowires.