The in-line and transverse forces acting on cylinders and the in-line force acting on spheres placed in a sinusoidally oscillating fluid have been measured. The periodic flow was generated in a u-shaped vertical water channel through the use of a pneumatic oscillator The drag, inertia and the lift coefficients as well as the total force coefficient have been determined through the use of Fourier analysis and found to depend on a period parameter. The results have shown that the transverse force acting on a cylinder in a periodic flow with zero mean velocity is as large as the in-line force. The frequency of the alternating transverse force depends on a period parameter and several frequencies may occur during a given period of oscillation of the flow. It is recommended that the experiments be extended to Reynolds numbers as large as 10^6 in a similar but larger apparatus. (Author)