We investigate the attitude of the solution of the Wentzell-Laplace boundary value problem with respect to shape deformations. On one hand, we prove the continuity of the solution under Lipschitz deformation of uniformly Lipschitz domains in the Euclidean space R^d. On the other hand, we demonstrate the continuity of the solution under the W^{2,∞} convergence of (2,∞)-Sobolev domains in R^d. After that, we discuss the convergence of the signed distance function in W^{1,p}(B) with 1 ≤ p ≤ ∞ with respect to the Hausdorff convergence of less regular domains, where B is a large ball containing the sequence of domains (Ω_{n})_{n∈N} and the limit set Ω, and we derive the following results: the uniformly Lipschitz case is enough for proving the convergence of the first order differential in L^p with 1 ≤ p < ∞; while in case p = ∞, we need to assume more regularity, the "positive reach" one. Moreover, to prove the convergence of the first order differential of the projection function on ∂Ω_{n} in L^p with 1 ≤ p ≤ ∞, we have to inject the (2,∞)-Sobolev regularity with the necessity of W^{2,∞} convergence of these domains.