Nuclear reactor core simulations involve several physics, especially in accidental transients.Neutron transport is needed to compute the power distribution. Thermal-hydraulics drives the cooling of the core. Fuel mechanics and heat transfer describe fuel state (including temperature). Mechanics allows to take into account deformations of the core. A lot of works have been done on coupling techniques betweenthese physics, but are usually based on separated codes or solvers. In this paper, we present an alternative approach the development of a shared solver for the coupled physics. A multiphysics solver is proposed for a time-dependent coupling between neutron diusion, heat transfer and linear mechanics. It is based on the finite element method and the Newton algorithm. A very simple application is given and shows the rightness of the developments and the relevance of the solver.