Tracking the displacement between the pre- and post-deformed radio-frequency (RF) frames is a pivotal step of ultrasound elastography, which depicts tissue mechanical properties to identify pathologies. Due to ultrasound’s poor ability to capture information pertaining to the lateral direction, the existing displacement estimation techniques fail to generate an accurate lateral displacement or strain map. The attempts made in the literature to mitigate this well-known issue suffer from one of the following limitations: 1) Sampling size is substantially increased, rendering the method computationally and memory expensive. 2) The lateral displacement estimation entirely depends on the axial one, ignoring data fidelity and creating large errors. This paper proposes exploiting the effective Poisson’s ratio (EPR)-based mechanical correspondence between the axial and lateral strains along with the RF data fidelity and displacement continuity to improve the lateral displacement and strain estimation accuracies. We call our techniques MechSOUL (Mechanically-constrained Second-Order Ultrasound eLastography) and -MechSOUL ( -norm-based MechSOUL), which optimize - and -norm-based penalty functions, respectively. Extensive validation experiments with simulated, phantom, and in vivo datasets demonstrate that MechSOUL and -MechSOUL’s lateral strain and EPR estimation abilities are substantially superior to those of the recently-published elastography techniques. We have published the MATLAB codes of MechSOUL and -MechSOUL at https://code.sonography.ai .