The mechanical unfolding of proteins is studied by extending the Wako-Saitô-Muñoz-Eaton model. This model is generalized by including an external force, and its thermodynamics turns out to be exactly solvable. We consider two molecules, the 27th immunoglobulin domain of titin and protein PIN1. We determine equilibrium force-extension curves for the titin and study the mechanical unfolding of this molecule, finding good agreement with experiments. By using an extended form of the Jarzynski equality, we compute the free energy landscape of the PIN1 as a function of the molecule length.