This paper presents a two-dimensional numerical algorithm for creep analysis of the elastic beams under uniform torsion. Torque is assumed to be constant during the whole creep process. Tangential stresses are calculated following the warping function distribution. Material creep behaviour is simulated using the effective stress function. Analysis takes in consideration the torque acting on cross-sectional surface independently on the beam length. The proposed numerical algorithm enables the stress analysis to be carried out regardless of the cross-sectional shapes. Viscoelastic effects of the material are modelled by the creep power law formula. Numerical algorithm was developed in Python code and its effectiveness is validated through the benchmark example.