This paper presents an analytical solution of the magnetic field in a coreless stator axial-flux permanent magnet (AFPM) machine, including axial, radial and circumferential components of the air-gap flux density. Based on the three-dimensional (3-D) analytical field solution, the paper also presents the analytical analysis of axial electromagnetic force of the rotor discs using Maxwell stress tensor method. The effect of some sizes on the axial electromagnetic force is analyzed. For the verification, 3-D finite element method (FEM) is accomplished to analyze the magnetic field and electromagnetic force. The solution and calculation are useful in design and optimization of coreless stator AFPM machines.