The propagation properties of surface plasmon polariton waves on graphene microtubes were investigated in this paper. A precise vectorial finite element modal solver that models graphene as a surface boundary condition is devised for the graphene microribbon case. The solver extracts the dispersion curves through the effective index of various supported modes, while its propagation length, compared to the microstrip's one, unveils a notable behavior of surface waves. Also, radial and axial electric field components are evaluated at different frequencies, indicating the strong confinement at the surface of graphene and the impact of the microtubes' diameter on the propagating modes.