Viscous resuspension of heavy particles in fully developed laminar flows in a horizontal pipe is investigated theoretically by extending the model used previously for unidirectional flows to cases in which all three velocity components are non-zero due to the existence of a secondary motion within the cross section of the pipe. The resulting mathematical system of equations was solved by employing the Galerkin finite-element method. The theoretically predicted velocity and concentration profiles for flow in a circular pipe were found to be in very good qualitative agreement with experimental results reported by others, even though the analysis did not make use of any adjustable parameters.