We consider the system of equations of Koiter shell theory - in a slightly simplified form - in the case when the limit problem for small thickness is parabolic, i.e., when the directions of the principal curvatures of the middle surface coincide everywhere. Under loadings that do not belong to the dual of the limit energy space, the solution energy grows without limit as the thickness tends to zero and concentrates on internal or boundary layers. We consider both the cases when the singular loadings are applied along a non-characteristic curve or along a characteristic curve. We prove convergence in the layers.