In this paper, we apply a rotated bilinear tetrahedral element to elastodynamics in R³. This element performs superior to the constant strain element in bending and, unlike the conforming linear strain tetrahedron, allows for row-sum lumping of the mass matrix. We study the effect of different choices of approximation (point- wise continuity versus edge average continuity) as well as lumping versus consistent mass in the setting of eigenvibrations. We also use the element in combination with the leapfrog method for time domain com- putations and make numerical comparisons with the constant strain and linear strain tetrahedra.