  We present a Poincar\'e covariant cascade algorithm based on the constrained
Hamiltonian dynamics in an $8N$-dimensional phase space to simulate the
Boltzmann-type two-body collision term. We compare this covariant cascade
algorithm with traditional $6N$-dimensional phase-space cascade algorithms. To
validate the covariant cascade algorithm, we perform box calculations. We
examine the frame dependence of the algorithm in a one-dimensionally expanding
system as well as the compression stages of colliding two nuclei. We confirm
that our covariant cascade method is reliable to simulate high-energy nuclear
collisions. Furthermore, we present Lorentz-covariant equations of motion for
the $N$-body system interacting via potentials, which can be efficiently solved
numerically.
