The periodic squeeze motion of a thin fluid film formed between two parallel planes is considered. The fluid is assumed to exhibit shear dependence and relaxation properties. Analysis shows that a time‐average super‐ or subambient pressure is generated which depends on the ratio of the periods of the compression and expansion strokes. Fluid consistency, shear rate exponent, plate geometry, and stroke affect the magnitude of the pressure values. The relaxation constant of the fluid enters only into the transient and the periodic parts of the squeeze film response. These effects are not obtained for Newtonian fluids or if the compression and expansion periods are equal.