A theoretical description of sinusoidal oscillation of an incompressible viscoelastic medium between fixed infinite parallel planes is presented. The mechanical properties of the viscoelastic medium under sinusoidal shear are expressed by a complex viscosity coefficient. The general equation for oscillatory motion of an incompressible viscoelastic medium is developed. The solution to this equation is obtained for rectilinear motion parallel to a pair of infinite planes. The equation for the velocity distribution between the planes is developed and several typical profiles are presented graphically. The equation for the acoustic impedance per unit area of plane is obtained. Functions from which the acoustic resistance and acoustic reactance may be determined are presented in graphical form for media which range from a perfect viscous fluid to a perfect elastic solid. The applicability of the theoretical results to oscillatory flow in rectangular tubes is discussed.