Previous studies about pure squeeze elastohydrodynamic lubrication (EHL) have disclosed a film profile with a central dimple. Two problems about pure squeeze EHL are numerically solved in this paper. One is for a very small initial impact gap, and the other is the response of a squeezed EHL conjunction under stepwise loads. None of them result in the familiar film with a central dimple, which can be attributed to the local squeeze effect generated in the periphery region. In the first problem, it has been found that when there is adequate oil present on the plate, with a decrease in the initial impact gap, a shallow circumferential dimple occurs at the periphery of the conjunction instead of the primary central dimple presented in previous studies. Correspondingly the minimum film thickness occurs at the central region. The effect of the initial impact velocity on the periphery dimple is also investigated. In the second problem, the response of a conjunction subjected to a prescribed stepwise load is studied. When the first step load is applied, a central dimple film is produced. When the applied load is increased with a second step load, a periphery dimple appears, similar to that in the first problem. The local squeeze effect for the present numerical periphery dimple has been observed in previous experiments under similar conditions.