Contactless and non-invasive estimation of mechanical properties of physical media from optical observations is of interest for manifold engineering and biomedical applications, where direct physical measurements are not possible. Conventional approaches to the assessment of image displacement and non-contact material probing typically rely on time-consuming iterative algorithms for non-rigid image registration and constitutive modelling using discretization and iterative numerical solving techniques, such as Finite Element Method (FEM) and Finite Difference Method (FDM), which are not suitable for high-throughput data processing. Here, we present an efficient deep learning based end-to-end approach for the estimation of continuum displacement and material compressibility directly from the image series. Based on two deep neural networks for image registration and material compressibility estimation, this framework outperforms conventional approaches in terms of efficiency and accuracy. In particular, our experimental results show that the deep learning model trained on a set of reference data can accurately determine the material compressibility even in the presence of substantial local deviations of the mapping predicted by image registration from the reference displacement field. Our findings suggest that the remarkable accuracy of the deep learning end-to-end model originates from its ability to assess higher-order cognitive features, such as the vorticity of the vector field, rather than conventional local features of the image displacement.