This investigation is concerned with the application of finite difference methods to the solution of thin elastic shallow shells. In particular, the ruled surface hyperbolic paraboloid is systematically studied to determine the influences of boundary conditions, geometric shape and material properties. The method developed for representing and solving the discretised system is suitable for use on digital computers of limited storage capacity and arithmetic speed. For all boundary types

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... d, solutions upon successively finer difference grids have demonstrated convergence to the analytic solution. A number of methods for accelerating this convergence were found to result .in an increase of total computational labour for a given numerical accuracy. The considerable differences in the behaviour of the degenerate clamped and free edged shells demonstrate the necessity of theoretical solutions embodying the influence of edge members. A number of numerical - physical analogues for the shell-edge member interaction are studied to ensure compatibility with the degenerate boundary conditions upon choice of suitable beam dimensions. The construction and testing of a "perspex" model with varied boundary and corner support conditions is described. Results from these tests are used as a basis for comparison with theoretical solutions and to provide additional information concerning the critical influence of the corner diagonal thrust. Conclusions from the theoretical and experimental investigations are in close agreement, and also verify solutions obtained in past research