This paper presents a solution method for obtaining the lateral hydrodynamic forces and moments on a submerged body translating at a yaw angle. The method is based on the infinite-fluid formulation of the free-surface random-vortex method (FSRVM), which is reformulated to include the use of slender-body theory. The resulting methodology is given the name: slender-body FSRVM (SB-FSRVM). It utilizes the viscous-flow capabilities of FSRVM with a slender-body theory assumption. The three-dimensional viscous-flow equations are first shown to be reducible to a sequence of two-dimensional viscous-fluid problems in the cross-flow planes with the lowest-order effects from the forward velocity included in the cross-flow plane. The theory enables one to effectively analyze the lateral forces and yaw moments on a body undergoing prescribed forward motion with the possible occurrence of cross-flow separation. Applications are made to several cases of body geometry that are in steady forward motion, but at a yawed orientation. These include the case of a long “cone-tail” body. Comparisons are made with existing data where possible.