In this paper, three types of unsteady flows of second-order fluids are considered, namely, flow caused by impulsive motion of a flat plate, flow induced by a constantly accelerating plane and flow imposed by a flat plate that applies a constant tangential stress to the fluid. The previous attempts made regarding these problems, by using the Laplace transform, have failed. In this paper, the sine and the cosine transforms are used to solve these problems and exact solutions for the velocity distributions are found in terms of definite integrals. It is shown that these exact solutions satisfy the initial and the boundary conditions and the governing equation. (C) 2002 Elsevier Science Ltd. All rights reserved.