As the magnets are embedded in a rotor for the interior permanent magnet (IPM) motor, the distribution of the armature reaction magnetic field is different from that of the surface permanent magnet motor (SPM) type. Various methods have been used for the magnetic field solution, including analytical methods based on the winding function and the Laplacian-Poisson equation. However, in the IPM motor, the boundary condition is too complicated for using the Laplacian-Poisson equation. What is more, the equivalent air-gap inverse function presented in literature is not suitable for the IPM motor. A new armature reaction magnetic field model is proposed for the IPM motor, considering the effect of the embedded magnet in the rotor, which is named a pole-cap effect in this paper. The proposed model is derived from the winding function theory, and the rotor magnetic motive force (MMF) function is employed to model the so-called pole-cap effect. The proposed model is used to predict the armature reaction field under a different type of stator MMF, such as different orientation of the excitation current as well as various MMF wavelengths. The calculation result is validated by the finite element analysis (FEA) and shows remarkable advantages over the traditional method. The new model proposed in the paper is quite useful for evaluating various IPM motor performances in an accurate and time-effective manner, such as inductance, stator core losses, and magnet eddy current losses. Complete demonstration of the method to calculate the aforementioned performance indices will be presented in a separate paper, and inductance calculation of a primitive winding is given as an example at the end of this paper.