Abstract
The boundary value problems of shallow shells theory can provisionally be separated into two kinds, internal (analysis of domes, beamless ceilings), and external boundary value problems (analysis of shells weakend by holes, i.e. problems of stress concentration). Both these directions have extensive bibliographies (see [1], say). Given below is a formulation of the fundamental boundary value problems from rather unique positions, similar in idea to the Koslov-Muskhelishvili conceptions in the plane problem of elasticity theory. Representations of the solutions of the boundary value problems are written down in series for simply and multiply connected domains.
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