To investigate the effect of lapping machine geometric errors on flank face roughness of diamond cutting tools, a mathematic model of lapping machine geometric errors and surface profile of tool flank face is built. The error propagation of lapping machine is modeled based on the theory of multi-body system. And a quantified relationship between machine errors and roughness is established using the algorithm of spline filter. The influence principle of end face and radial errors of spindle and sway, and the straightness error of reciprocates on roughness are analyzed. The result shows that the influence proportion of spindle, sway and reciprocating geometric moving errors on roughness are 98.18%, 1.59% and 0.23% respectively, hence roughness of flank face is mainly affected by spindle end face and radial errors which offers a guidance to the design and manufacturing of lapping machine and optimization of lapping technics for diamond cutting tools.