This piece of work deals with the viscous stability of trailing line vortex. The perturbations are three dimensional and the viscous effects were encountered. The eigenvalue problem was solved by implementing a pseudo-spectral approach in MATLAB environment. The code was confirmed through comparing the results with those available in the literature, produced with Bachelor’s vortex model as base flow. The code was afterwards used to investigate the stability of trailing line vortex where the azimuthal component of the base flow was the one of Vatistas’ vortex model. The stability of the linear modes (Kelvin’s waves) was investigated for axisymmetric and asymmetric disturbances. Results for the temporal viscous unstable modes were provided. The influence of swirl parameter and Reynolds number on the growth rate, phase speed and amplitude, of the perturbations were studied.