This work introduces and compares two different CAD-based mesh deformation methods. The methods are used within an adjoint structural shape optimization, which is part of an evolving CAD-based adjoint multidisciplinary optimization framework for turbomachinery components. During an optimization, the CAD geometry is updated at each design iteration, such that the structural mesh has to be deformed appropriately. The mesh is deformed in three stages. First, the nodes along the edges of the outer mesh are displaced to match the shape of the CAD edges, which are given by B-spline curves. Next, the remaining outer mesh nodes are displaced to match the shape of the CAD faces, which are given by B-spline surfaces. Finally, the outer mesh node deformations are used to solve for the inner node deformations using either an inverse distance interpolation or the linear elasticity analogy. Coupling the mesh deformation with an adjoint structural solver enables gradient computations of structural constraints with respect to CAD design parameters. To compare the robustness of the two mesh deformation methods, a CAD-based structural shape optimization using each method was performed.