Sensitivity expressions for a general performance criterion (cf. an integral functional) with respect to shape have been derived for viscoelastic solids under transient response. Differential and integral types of constitutive equations are considered in the study, in which a continuum approach is adopted. By using the material derivative concept and the adjoint variable method the sensitivity of the general integral functional is obtained in terms of primary and adjoint functions. A simple example problem is also provided to check the results by comparing them with those found by a direct differentiation.