Redfield theory is applied to investigate the photoinduced dynamics at a conical intersection (the so-called system) which is weakly coupled to a thermal environment (the so-called bath). The dynamics of the system is described by a two-state three-mode model Hamiltonian, chosen to represent the S-1(n pi*)-S-2(pi pi*) conical intersection in pyrazine. Dissipative effects are introduced through a bilinear coupling of the system vibrational modes with a harmonic bath, which represents the remaining vibrational degrees of freedom of the molecule and/or interactions with a condensed-phase environment. The Redfield equations for the reduced density matrix are solved numerically without further approximations. From the reduced density matrix the time evolutions of electronic-state populations and vibrational coherences are obtained, as well as time-dependent probability densities of individual vibrational modes. The results provide a visualization of the essential features of the ultrafast (time scale of 10 fs) internal-conversion process at the conical intersection and the ensuing vibrational cooling process on the lower adiabatic potential-energy surface. The effect of vibrational damping on the linear optical absorption spectrum is also investigated.