  In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and
Lagrangian systems. We study the complete solutions, particularize for Rayleigh
systems and present some examples. Additionally, we present a method for the
reduction and reconstruction of the Hamilton-Jacobi problem for forced
Hamiltonian systems with symmetry. Furthermore, we consider the reduction of
the Hamilton-Jacobi problem for a \v{C}aplygin system to the Hamilton-Jacobi
problem for a forced Lagrangian system.
