For four decades, since W. Helfrich's pioneering study of smectic A liquid crystals in 1973, continuum elastic models (CEMs) have been employed as tools to understand the energetics of protein-induced lipid bilayer deformations. Among the assumptions underlying this use is that all relevant protein-lipid interactions can be included in the continuum representation of the protein-bilayer interactions through the physical parameters determined for protein-free bilayers and the choice of boundary conditions at the protein/bilayer interface. To better understand this assumption, we review the general structure of CEMs, examine how different choices of boundary conditions and physical moduli profiles alter the predicted bilayer thickness profiles around gramicidin A (gA) and mitochondrial voltage-dependent anion channels (VDAC), respectively, and compare these profiles with those obtained from all-atom molecular dynamics simulations. We find that the profiles differ qualitatively in the first lipid shell around the channels, indicating that the CEMs do not capture accurately the consequences of the protein-induced local changes in lipid bilayer dynamics. Therefore, one needs to be careful when interpreting the results of CEM-based analyses of lipid bilayer-membrane protein interactions.