It is well known that the quality of finite element (FE) simulations depends strongly on the mesh that is used. In particular, the shape of the elements has a major influence on the numerical results. Results from simulations with distorted meshes usually deviate significantly from those obtained with regular meshes. However, in many practical applications, meshes with distorted elements are unavoidable due to the geometry of the simulated structure. To address this issue, various FE formulations based on the Petrov-Galerkin method have been developed in recent years. In contrast to the Bubnov-Galerkin method, which is commonly used in most FE formulations, the Petrov-Galerkin method employs different ansatz spaces for the test and trial functions. In elastostatic simulations, such formulations typically show a lower sensitivity to distorted meshes. However, extending these mesh distortion insensitive Petrov-Galerkin FE formulations to time-dependent problems is not straightforward. For the case of linear elastodynamics, Wang and Hillman [1] have already shown that the use of non-symmetric mass and stiffness matrices - as they naturally arise in Petrov-Galerkin formulations - can lead to an unbounded energy growth over time and, consequently, to unstable simulations. Focusing on the 8-node Petrov-Galerkin FE formulation UQ8* [2], we therefore investigated and evaluated different non-standard approaches for the extension of this formulation to the dynamic regime. A novel approach, developed specifically with the objective of satisfying the global energy balance, yielded particularly good results. The core idea of this approach, which we present in more detail in this contribution, is to introduce the velocity field as an independent variable and to enforce its relationship with the displacement field through a specific constraint. We demonstrate that stable simulations are possible with the resulting formulation and that it actually exhibits improved properties in terms of mesh distortion sensitivity compared to a standard formulation. REFERENCES [1] Wang J., Hillman M. C., Temporal stability of collocation, Petrov-Galerkin, and other non-symmetric methods in elastodynamics and an energy conserving time integration, Comput. Methods Appl. Mech. Eng., Vol. 393, pp. 114738, 2022. [2] Xie Q., Sze K. Y., Zhou Y. X., Modified and Trefftz unsymmetric finite element models, Int. J. Mech. Mater. Des., Vol. 12, pp. 53–70, 2016.