<p>The paper addresses the computation of the gradient of the misfit function in inverse problems for determining the geometric characteristics of elastic layered packages located on a Pasternak elastic foundation. Calculating such a gradient is crucial for the efficient parameterization of the inverse problem, as well as for tasks related to “Optimization” and “Uncertainty Quantification”. The observed/simulated data of the inverse problem consists of ray displacements at specific points on the upper surface of the package. The layers of the package are assumed, in the general case, to be anisotropic and inhomogeneous; the interfaces between the layers are curved, as is the lower surface of the package resting on the elastic foundation. The incorporation of geometric characteristics into the model of the inverse problem is based on introducing parameterization into the mapping used for constructing regular grids for each layer. The gradient components are determined using the Adjoint State Method within the framework of the Block-Parametric Approach, employed in the Information-Probabilistic (Bayesian) paradigm for analyzing inverse problems. This approach allows for the effective variation of different parameterization schemes for the problem, the identification of anomalous values in observed data (“outliers”), and the refinement of prior distributions’ parameters. The discretization of the forward and adjoint problems used to compute the gradient components, as well as the application of a multigrid iterative method for their approximate solution, is also considered.</p>