In this paper we show that problems concerning the development of a boundary layer on a semi-infinite plate when the outer flow speed is of the form U = (1 + ct)^ba, and on a cylinder when the outer flow speed has the forms U = ct^αx^m and U = (1 + ct)^bax^m, are self-similar. We present the results of numerical calculations for various values of α, b, and m. We consider the problem of a stepwise nonstationary heating of a plate, impulsively set into motion in an incompressible fluid; we show that this problem is self-similar and obtain its solution numerically.