This talk presents a new finite element for transient dynamic computations in solids, amenable to be used with triangular and tetrahedral grids [1]. Particularly in the case of nearly or fully incompressible materials, low-order computational methods for solid mechanics are for the most part confined to grids composed of quadrilateral and hexahedral elements. This is due to the fact that there are no simple finite element formulations that are stable on triangular and tetrahedral grids in the transient case. However simplicial grids are very important in computing, as they allow for very fast automated meshing algorithms, which cut the grid generation time (and ultimately the overall design and analysis time) by orders of magnitude. The method discussed in this talk is an attempt to address the issue of stability and accuracy in computations with simplicial linear finite elements in solid dynamics. It utilizes the simplest possible finite element interpolations: Piece-wise linear continuous functions are used for displacements and pressures (P1/P1), while the deviatoric part of the stress tensor is evaluated with simple single-point quadrature formulas. This approach takes inspiration from previous work of the first author in the case of compressible fluid dynamics in Lagrangian coordinates [2]. The variational multiscale stabilization eliminates the pressure checkerboard instabilities affecting the numerical solution in the Stokes-type operator that arises in solid dynamics computations. The formulation is extended to elastic-plastic, and viscoelastic solids. Extensive numerical tests are presented. Because of its simplicity, the proposed element could favorably impact complex geometry, fluid/structure interaction, and embedded discontinuity computations. Time permitting, a number of preliminary results on fluid-structure interaction problems will also be presented.