This paper presents a methodology for the inverse identification of linearly viscoelastic material parameters in the context of steady-state dynamics using interior data. The inverse problem of viscoelasticity imaging is solved by minimizing a modified error in constitutive equation (MECE) functional, subject to the conservation of linear momentum. The treatment is applicable to configurations where boundary conditions may be partially or completely underspecified. The MECE functional measures the discrepancy in the consti-tutive equations that connect kinematically admissible strains and dynamically admissible stresses, and also incorporates the measurement data in a quadratic penalty term. Regularization of the problem is achieved through a penalty parameter in combination with the discrepancy principle due to Morozov. Numerical results demonstrate the robust performance of the method in situations where the available measurement data is incomplete and corrupted by noise of varying levels.