An original approach to morph meshes including slip planes is proposed. Extending the classical interpolation scheme based on Radial Basis Functions (RBF), it preserves the linear property, linking the deformation response to the known displacements, underlying the RBF formalism. No post-correction stage, nor extra not-moving control points, are required to enforce in plane displacements. Accuracy and robustness are evaluated for a 2D configuration where a shock-wave impinges on a cross-flow flexible panel. Analysis is based on deformation quality metrics derived from the displacement field gradient, keeping the proposed approach free from connectivity information. 3D applications are briefly illustrated by the tip of an aero engine fan subjected to conjugated parameterized variations of tip clearance and stagger angle.