In the context of non-destructive evaluation, Ultrasonic Testing (UT) is popular across numerous industrial fields. Building efficient numerical schemes for high-frequency transient wave propagation to model the UT experiments is relevant and can be challenging depending on the considered configurations. Combining high-order lumped finite elements with explicit time schemes is a popular approach [Cohen2003] for either inviscid or visco-elastic models [Imperiale2020]. Such schemes have proven to be efficient and fast when considering quasi-uniform meshes. However, when dealing with non-uniform meshes, the CFL condition is constrained by the most degenerate element of the mesh. We can encounter such meshes when dealing with “unfortunate” CAD input file, in particular when meshing with quadrilaterals or hexahedra. In fact, most meshing softwares can produce distorted elements when confronted with sharp-angled CAD, which leads to a deteriorated CFL condition. Non-uniform meshes may also appear when dealing with particular applications, e.g., multiple inclusions in an otherwise sound domain, which can be very close to each other and produce very small elements in-between them. Thus, in such contexts, the resolution of the problem can be quite time-consuming due to the CFL becoming drastically stringent. In this work, we propose to adapt the locally implicit time schemes [Rylander2002] to visco-elastic models in order to obtain robust fully discrete schemes w.r.t. mesh non-uniformities. We can prove using energy arguments that the global CFL does not depend on the problematic cells anymore, and can be greater than a fully-explicit scheme, decreasing the number of iterations for a fixed time window. However, this implies solving locallized linear systems at each time step, which can be a costly process, especially in 3D. Thus one needs to carefully balance the cost of the resolution of linear systems with the gain in the CFL condition in order to increase the overall performance of the locally implicit scheme compared to the fully-explicit scheme. We present 2D and 3D numerical test cases for visco-elastic models in a non-destructive testing context.