Many attempts made in modelling stratified two-phase flow for predicting the operational flow characteristics (pressure drop, holdup, etc.) assume mostly plane interface between the phases. Obviously, the interaction between the stratified layers and the resulting flow characteristics may be significantly affected by the configuration of the interface. Moreover, complete analytical solutions for stratified flows in circular conduits are not yet available even for laminar flows with plane interface and most of previous studies resort to average two-fluid modelling. The present study presents analytical solutions for laminar stratified two-phase flows in pipes with plane and curved interfaces.