Numerical simulations shed light on control of shear elastic wave propagation in plates structured with inertial resonators. The structural element is composed of a heavy core connected to the main freestanding plate through tiny ligaments. It is shown that such a configuration exhibits a complete band gap in the low frequency regime. As a byproduct, we further describe the asymmetric twisting vibration of a single scatterer via modal analysis, dispersion, and transmission loss. This might pave the way to functionalities such as focusing and self-collimation in elastic plates.