Rigidity of feed system with ball screw in NC lathe has a major influence on loss of momentum and positioning precision. Based on the spring mechanics model and the quality of the feed system, the analytic formulation for the effect of the transition and torsion rigidity of the feed system on the loss of momentum have been given. The analytic formulation for position error have been given, too. Theoretic basis for designing the structure, reducing loss of momentum and increasing positioning precision of feed system has been provided. Moreover, analysis and calculation have been made in combination with an actual example, and significant effect has been obtained.