This paper deals with an original simultaneous localisation and map building paradigm (SLAM) based on the one hand on the use of an omnidirectional stereoscopic vision system and on the other hand on an interval analysis formalism for the state estimation. The first part of our study is linked to the problem of building the sensorial model. The second part is devoted to exploiting this sensorial model to localise the robot in the sense of interval analysis. The third part introduces the problem of map updating and deals with the matching problem of the stereo sensorial model with an environment map, (integrating all the previous primitive observations). The SLAM algorithm was tested on several large and structured environments and some experimental results will be presented.