Relevant performance indicators of built machines can significantly differ from the original design with exact dimensions as a consequence of manufacturing or assembly tolerances. Nevertheless, tolerance analysis of electrical machines represents a major challenge in terms of computational burden, and is currently being addressed in the technical field. This paper presents a continuous-domain semi analytical method (CDSM) to obtain the cogging torque of Axial Flux Permanent Magnet (AFPM) machines in presence of manufacturing tolerances. By means of the CDSM and a reduced number of FE simulations, the cogging torque signal of several faulty designs can be obtained. The proposed method was validated by means of several FE-only simulations; and was used to conduct a statistical tolerance analysis of a 12-slot 10-pole two-stator one-rotor AFPM machine. The CDSM provided acceptable accuracy and succeeded to significantly drop the computation time required for carrying out an extensive tolerance analysis of AFPM machines.