The development of high-temperature superconducting (HTS) electrical machines results in applications of various fields, as they have higher efficiency and power density. Numerical modeling of superconducting electrical machines is usually performed by finite element method based their electrical behavior, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> -Formulation of the Maxwell's equations is one of the models that are used tremendously due to its high flexibility and simplicity. Axial field machine (AFM) is a machine topology with higher efficiency and power density, but with more complexity when modeling. This paper proposed a new 2D model for the superconducting AFM, where the superconducting coil is simulated with a 2D infinitely long model, this model also divides the electrical machine into two parts: the superconducting parts (HTS coils, bulks, etc.) and non-superconducting parts (e.g., conventional conductors, machine structure). This paper compares the results of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H-A</i> Formulation and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T-A</i> Formulation with this approach, which requires appropriate boundary conditions and continuity between the two regions, along with correct modeling of fixed and moving parts of the electrical machine, where the geometry of this model is based on a linear synchronous machine, which means the rotor is moving linearly instead of rotation.