Experimental results are reported for the constant‐force squeezing of three highly viscous polymers. Profiles for the plate separation versus time were measured with the use of a modified materials testing system. Two polybutenes were tested at 25 °C, and a low‐density polyethylene melt (IUPAC sample X) was studied at 150 °C. Measured half‐times show that the polybutenes behave as inelastic fluids with viscosities that decrease slightly with shear rate. In slow squeezes the experimental results agree with the predictions of Newtonian fluid theory corresponding to the available viscosity measurements. The behavior of LDPE X is described by the CEF model in both slow and fast squeezes. Although shear rates are as high as 1000 s−1, the elastic effects for LDPE X are small compared to viscous effects.