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Aerospace, die, and mold industries utilize parts with sculptured surfaces, which are machined on five-axis computer numerical controlled machine tools. Accurate path tracking for contouring is not always possible along the desired space curves due to the loss of joint coordination during the five-axis motion. This two-part paper presents modeling and robust control of contouring errors for five-axis machines. In Part I, two types of contouring errors are defined by considering the normal deviation of tool tip from the reference path, and by the normal deviation of the tool axis orientation from the reference orientation trajectory defined in the spherical coordinates. Overall contouring errors are modeled during five-axis motion that has simultaneous translation and rotary motions. The coupled kinematic configuration and the rigid body dynamics of all five drives are considered. The contouring error model is experimentally validated on a five-axis machine tool. The error model developed in this paper is then used for simultaneous, real-time robust control of all five drives in Part II.