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 ε^1/2 where ε denotes the (half-)thickness of the shell. Both 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 like for plates. Using these expansions we obtain sharp estimates between the two models in various norms.