[en] Surface and internal quality of continuous casts depends very much on the behaviour of the strand in the mould. Among the parameters likely to influence this behaviour, the mould taper takes a prominen tpart. In order to understand better the influence of this parameter, we build up a thermal-mechanical finite element model. A slice of the strand is modelled and its evolution is observed. The main results are temperature field and solidification evolution, stree, strain and strain rate fields and losses of contact and returns to contact analysis. The model includes an elastic-viscous-plastic law, to describe the behaviour of steel from liquid to solid state, a thermal-mechanical element that takes into account thermal expansion and mechanical behaviour of the strand, a unilateral contact element, z mobile rigid boundary element to model the mould and its taper and an adapted loading element to model the ferrostatic pressure according to the liquid or solid state. This paper presents the first results obtained with an relatively simple section ( a125 mm square billet). Now the model is used with more complex section (beam blanks) and its validation is going on.