The path following technique known as ’the arc length method’ has evolved over the past decade into a commonly used tool in nonlinear finite element analysis. Variations of this method have originated from a number of other workers. This paper presents a new general formulation for all arc length procedures. A derivation is given based on orthogonality principles which provides a new perspective illustrating the relationship between the existing and proposed path following techniques. A simplified procedure, obtained directly from the new general formulation, provides the same results as M. A. Crisfield’s explicit iteration procedure [Comput. Struct. 13, 55-62 (1981; Zbl 0479.73031)] with a reduction in computational effort. Practical application of this theory is demonstrated using a numerical example of a recticulated shell structure.