  The distribution of magnetic induction in Meissner state with finite London
penetration depth is analyzed for platelet samples of rectangular cross-section
in a perpendicular magnetic field. The exact 2D numerical solution of the
London equation is extended analytically to the realistic 3D case. Data
obtained on Nb cylinders and foils as well as single crystals of YBCO and BSCCO
are in a good agreement with the model. The results are particularly relevant
for magnetic susceptibility, rf and microwave resonator measurements of the
magnetic penetration depth in high-Tc superconductors.
