When steel grillages are subjected to variable repeated loads which exceed elastic ranges, the structure may behaves as if it were within elastic range. Such a phenominon is defined as a shakedown. Matrix and Newton Raphson method are used for the shakedown analysis of a grillage structure. Plasticity of the structure is affected by the combined actions of bending moment and torsion. A method of identifying whether incremental collapse or alternating plasticity is the governing mode of failure is given. Based on the formulation presented, a FORTRAN computer program named SHLA was written to carry out the shakedown analysis of general planar grillages. Finally, two examples of typical bridge grillages are presented primarily to demonstrate the effect of including torsion in the analysis and also to indicate how easy it is to perform such analysis for practical engineering applications.