The Boundary Element Method (BEM) has been used to evaluate the integral and local flow properties of two-phase laminar-laminar stratified flow in a pipe for interface shapes determined by exact solution of the Young-Laplace equation. Results are presented for the volumetric flow rates, the interface and wall shear stresses and the velocity profiles on the interface and through the cross-section of the pipe. For the case of a flat planar interface, the results obtained from the BEM were compared against those from the analytical solution for a 50% holdup (i.e. with a flat interface passing through the horizontal axis) and with previous numerical solutions obtained using the bipolar coordinate system. Comparisons for the case of a circular interface were made with the Fourier integral method described by others. The solutions from the boundary integral method agree very well with these published results for special cases. Solutions are presented for a range of parameter values. The interface shape is determined by the Bond number, holdup or contact angle. The flow is controlled by these parameters, as well as the viscosity ratio, and the pipe inclination, which determines the relative driving forces on the two fluids. It is concluded that the BEM offers great flexibility and accuracy in addressing this class of flows. (C) 2002 Published by Elsevier Science Ltd.