A one-dimensional purely-viscous model that includes slip at solid boundaries is proposed to study the flow of polymeric materials when compressed between two approaching parallel surfaces. A squeeze-flow rheometer was designed and built to compress polymer melts under controlled conditions of constant closing speed and constant applied force for different conditions at the polymer-solid interface. One of the purposes of this study was to investigate how the interface conditions influence the flow field during squeezing. The experimental findings revealed that the model can adequately predict the squeezing farce for slow squeezing of relatively thin samples. For fast squeezing, however, the experiments appear to suggest the need of including elongational effects in the modelling of the material behavior.