AbstractWe consider an elliptic variational-hemivariational inequality 𝓟 in a reflexive Banach space, governed by a set of constraintsK, a nonlinear operatorA, and an elementf. We associate to this inequality a sequence {𝓟n} of variational-hemivariational inequalities such that, for eachn∈ ℕ, inequality 𝓟nis obtained by perturbing the dataKandAand, moreover, it contains an additional term governed by a small parameterεn. The unique solvability of 𝓟 and, for eachn∈ ℕ, the solvability of its perturbed version 𝓟n, are guaranteed by an existence and uniqueness result obtained in literature. Denote byuthe solution of Problem 𝓟 and, for eachn∈ ℕ, letunbe a solution of Problem 𝓟n. The main result of this paper states the strong convergence ofun→uinX, asn→ ∞. We show that the main result extends a number of results previously obtained in the study of Problem 𝓟. Finally, we illustrate the use of our abstract results in the study of a mathematical model which describes the contact of an elastic body with a rigid-deformable foundation and provide the corresponding mechanical interpretations.