We study the behavior of solutions of five different boundary value problems for the Reissner-Mindlin plate model emphasizing the structure of the dependence of the solutions on the plate thickness. The boundary value problems considered are those modelling hard and soft clamped plates, hard and soft simply supported plates, and free plates. As proven elsewhere, the transverse displacement variable does not exhibit any edge effect, but the rotation vector exhibits a boundary layer for all the boundary value problems. The bending moment tensor and shear force vector have more pronounced boundary layers. The structures of each of these boundary layers are explored in detail. In particular, their strength depends on the type of boundary conditions considered.