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We investigate solutions of the two-dimensional Koiter model and of the three- dimensional linear shell model in the case where the shell is clamped and its mean surface is elliptic. For smooth data. these solutions admit multiscale expansions in powers of ε½ where ε denotes the (half-)thickness of the shell. Roth expansions contain terms independent of ε and boundary layer terms exponentially decreasing with respect to r/ √ε, with r the distance to the boundary of the mean surface. The expansion of the three-dimensional displacement contains supplementary boundary layers. exponentially decreasing with respect to r/ε as for plates. Using these expansions we obtain sharp estimates in various norms. [ABSTRACT FROM AUTHOR]