The field of shear wave ultrasound elastography has proposed several methods for measuring tissue elasticity by exciting a shear wave in the tissue using acoustic radiation force and measuring the shear wave velocity using pulse-echo ultrasound. In plate-like organs such as the myocardium, the shear and the compressional waves produced by the acoustic radiation force interfere to form Lamb waves. Relating the Lamb wave velocity and tissue elasticity requires the complicated Lamb wave dispersion theory. Two-dimensional (2-D) tracking of the medium deformation allows for removing of the compressional wave contributions. Theory showing the curl of a 2-D particle motion followed by the direct inversion (CDI) in a plate is developed. A finite element model (FEM) of three elastic plates with the shear moduli of 25 kPa, 36 kPa and 49 kPa surrounded by semi-infinite media with the shear modulus of 1 kPa was used to test the theory. The CDI-based elasticity estimates were in excellent agreement with the theoretical values. A mechanical shaker was used to excite plane shear waves in a phantom consisting of a 7 mm 2% agar plate embedded between two semi-infinite 5% gelatin phantoms. Two linear array transducers were used to track the motion perpendicular and parallel to the excitation axis. A 12 × 6 × 4 cm3 agar cube from the same batch as the plate was made to measure the shear wave velocity. The shear wave velocity in the agar plate using the CDI method was in good agreement with the shear wave velocity measured in the cube phantom.