An extended Hamiltonian approach to conduct isothermal-isobaric molecular dynamics simulations with full cell flexibility is proposed. The components of the metric tensor are used as the fictitious degrees of freedom for the cell, thus avoiding the problem of spurious cell rotations and artificial symmetry breaking effects present in the original Parrinello-Rahman scheme. This is complemented by the Nose-Poincare approach for isothermal sampling. The combination of these two approaches leads to equations of motion that are Hamiltonian in structure, and which can therefore be solved numerically using recently developed powerful symplectic integrators. One such integrator, the generalized leapfrog, is employed to provide a numerical algorithm for integrating the isothermal-isobaric equations of motion obtained.