There are currently two main trends in solving magnetic field problems, numerical methods, of which the Finite Element Method (FEM) is undoubtedly the most popular, and analytical methods, of which there is a great diversity of approaches. The main advantage of numerical methods is their flexibilit y in modeling complicated geometries; however, its calculation times are generally considerable. Analytical methods attain very short calculation times by sacrificing flexibility. This paper presents the mathematical formulation of a new linear surface element for the semi-analytical solution of axisymmetric magnetic field problems. The importance of this formulation is that it is capable of dealing with arbitrary geometries while retaining the flexibility of numerical methods with considerably shorter calculation times. The results of the application of the proposed formulation to a case study are presented in the validation section. The results obtained are compared with those calculated with FEM showing an excellent agreement between them.