We report on a new numerical computation of the surface tension between domains of opposite magnetisation in the lsing model in two and three dimensions. The method is quite general and can be applied to any statistical-mechanics model. It is based on a partition of the lattice into two halves, which are slowly driven from one magnetization state to the other. The free energy of the interface is the result of the difference between the total free energies of the homogeneous and of the mixed phases. We first test the method in the two-dimensional (ferromagnetic) Ising model by comparing with the Onsager solution. We then compare the results in three dimensions with previous Monte Carlo simulations of thermal equilibrium and of decays via nucleation. The three-dimensional results are also used in the computation of the universal amplitude combination that involves the correlation length and the surface tension. Near the critical temperature, the numerical results agree well with measurements performed in the laboratory.