A tape placement method and apparatus for producing laminated articles from composite tape. The tape placement apparatus builds plies of a laminated article by laying courses of composite tape along natural or untensioned paths of a compound contoured surface. The natural paths are determined by a path generation routine which incrementally fits an untensioned path to a compound curved surface and outputs the data as a desired path for a tape course. The natural paths are generated as nonmachine specific geometric data which are translated into a machine instructions which cause controlled motions of the tape laying head of the tape placement apparatus. The translation into machine instructions includes an alignment process whereby variations in the orientation of the contoured surface can be corrected. The machine instructions are transmitted as desired positions to a adaptive controller which positions a tape laying head of the placement apparatus based on the difference between the desired positions and the actual positions of the tape head.