Relationship between machining-induced residual stress and machining parameters is “one-to-many” relationship, in order to compute machining parameters using known residual stress to obtain desired residual stress distribution, method of parameter inversion from the subject of Geophysics was introduced. Then based on previous works on analytical modeling and mechanism analysis of machining-induced residual stress, the effects of feed rate and cutting speed on depth of highest compressive residual stress are considered as linear superposition. Therefore, theory of linear inversion could be introduced to establish linear equations of residual stress increments that caused by increments of different machining parameters, to compute feed rate and cutting speed under known condition of depth of highest compressive residual stress. The computed residual stress profiles using the computed feed rate and cutting speed show that depth of computed maximum compressive residual stress is consistent with desired values and experimental results. The proposed method of parameter inversion for machining provides a new method to compute desired machining parameters quantitatively in order to achieve desired residual stress distribution, which is significant for machining parts with higher quality of surface integrity.