We consider geometric problems concerning the wave propagation in plates and circular cylindrical shells with edge of an arbitrary shape. We give a method for the choice and the construction of a coordinate system on the middle plane of the plate which allows to take into account the shape of the plate edge: in this case the length of the arc of the normal and the parameter of the edge line are chosen as coordinates. In case of a circular cylindrical shells with the edge of an arbitrary shape a semi-geodesic coordinate system can be constructed on the middle surface. In order to find the solution of the edge effect equation we apply the Laplace transform and the method of exponential representations in the space of transforms.
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