Solutions to the two-dimensional equations of motion for steady laminar flow in grooves are obtained by the Galerkin boundary method. The two independent parameters which characterize the flow configuration are the half angle of the liquid-filled triangular groove and the contact angle of the shear-free meniscus. The analytical results include dimensionless velocity contours, average velocity, hydraulic diameter, and area. The friction factor coefficient K, where f = K/Re and Re is Reynolds number based upon hydraulic diameter, is also found. Results are reported for channel half angles from 5–60 deg and contact angles from 0.1 deg to the complementary angle (full groove condition). Comparisons with analysis and experimental data for the full groove are made and found to be excellent.