How do I set up a mass spring equation with time delays between masses.

In popular structural and spring mass models, the transmission of forces through members is assumed to be instantaneous, but stress propagates at the speed of sound. I want to set up a linear mass-spring model or structural rod model with a force applied at one end with roughly 10,000 elements that accurately represents the time delay between nodes. I could apply the force to the first node for time step 1, calculate stress, strain, displacements, velocities, and accelerations, and then use the calculated values as the input for the next time step, but this would require many tedious iterations. Anyone know how to build time delays into the matrix methods?