A new and accurate method is described for deriving finite strains from moiré displacement patterns. The components u and v of the displacements at the mesh points of a Lagrangian co-ordinate network are estimated from the moiré fringes. In the neighbourhood of a point, where the strains are to be calculated, two algebraic functions are determined, approximating as closely as possible to the two sets of estimated u and v values. The strains are then calculated from the partial derivatives of these two functions. The procedure is repeated for all points at which the strains are required. When this procedure is applied to a great number of points the use of a computer becomes a practical necessity. Once the formulae have been programmed, the operator has only to estimate the u and v values at the mesh points of the co-ordinate network and to feed this set of numbers to the computer. This new method thus allows a considerable gain in time and brings about an improvement in accuracy compared with other methods.