This paper proposes a method for the semi-analytical solution of the coupled linear differential equations that describe the linear modal coupling arising in few mode fibers (FMFs) due to waveguide imperfections. The semi-analytical solutions obtained can be used for the modification of the split step Fourier method to include the respective linear effects. Considering a fiber with six linearly polarized modes (or ten modes, taking into account the degenerate versions) the solutions obtained proved to be accurate when compared to the numerical solutions obtained through the Runge-Kutta-Fehlberg method.