The known limitations of classical mesh and nodal methods of analysing linear electrical circuits are described before considering an established modification of the nodal approach. The method, known as 'modified nodal analysis', has none of the limitations of the basic nodal technique and is well suited both to symbolic and numeric analysis of complex circuits using modern matrix-based software. The simplicity of incorporating into the matrix equations all types of passive and active circuit elements is demonstrated and examples are used to illustrate further the efficacy of the method. It is emphasised that the absence of this circuit analysis technique from many academic engineering courses is totally at variance with its widespread application in modern circuit simulation packages.