An axisymmetric finite element solution method is developed for axial wave propagation through a series of threaded connections in rock drills. A piston impacts axially on a string of rods held together by threaded joints and the wave propagates through these joints before reaching the bit. The energy lost in the joints limits the maximum effective depth of the drill. Several computational techniques are used to efficiently model the problem. Non-reflecting boundaries are used to numerically absorb the waves as they exit a joint. The stored waves are then re-initiated into the next joint eliminating modeling of the entire assembly of rods. The preload in the threads is modeled by shrinking the threaded sleeve onto the rods. A new dynamic relaxation damping scheme is used which starts with an undamped model and then increases the damping until the solution converges. This method converges more rapidly than the standard constant damping. / Master of Science