A set of non-linear simultaneous differential equations is developed which describes the behaviour of certain types of highly curved shells. Certain simplifying assumptions are made for which justifying arguments are put forward and the resulting equations remain generally applicable within wide limits of initial shell curvature and of deformation. Boundary conditions are developed for a number of simple cases and the methods available for the numerical solution of the equations are briefly discussed. Experimental comparisons and detailed descriptions of numerical procedures are not given here but will be the subject of a further paper.
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