The rheology of submicron thick polymer melt is examined under high normal pressure conditions by a recently developed photobleached‐fluorescence imaging velocimetry technique. In particular, the validity and limitation of Reynold equation solution, which suggests a linear through‐thickness velocity profile, is investigated. Polybutene (PB) is sheared between two surfaces in a point contact. The results presented in this work suggest the existence of a critical pressure below which the through‐thickness velocity profile is close to linear. At higher pressures however, the profile assumes a sigmoidal shape resembling partial plug flow. The departure of the sigmoidal profile from the linear profile increases with pressure, which is indicative of a second‐order phase/glass transition. The nature of the transition is confirmed independently by examining the pressure‐dependent dynamics of PB squeeze films. The critical pressure for flow profile transition varies with molecular weight, which is consistent with the pressure‐induced glass transition of polymer melt.