The problem of squeezing flow of a viscoelastic fluid between two parallel disks approaching each other at constant speed is examined theoretically and experimentally. Theory treats a nonlinear viscoelastic constitutive equation due to Wagner. Experiments are performed with aqueous polyacrylamide solutions. The data exhibit significant deviations from purely viscous but non‐Newtonian performance, and the Wagner model shows good agreement with several features of the data.