The European Solar Telescope (EST) is a 4-meter class solar telescope led by the Instituto Astrofísico de Canarias that will be erected in La Palma Island. The design process is now approaching the Preliminary Design Review. The EST, as solar telescope, will have singularities that make its design differ from other telescopes. Telescope configuration, high solar radiation, absence of dome during observation, besides other elements, will have a strongly impact to the system design. One of the telescope critical elements is the primary mirror and its support. Along the last months, the preliminary design of these items has been performed. Critical aspects as mirror heat rejection, surface temperature and homogeneity, shape error, wind perturbations, etc., have had strong influence in the design solutions, pushing to use, for example, the thinner solid meniscus mirror never manufactured supported by 80 tripods over electromechanical actuators. This paper presents the design of the primary mirror and its support, presenting the adopted design solutions to cope with the different difficulties as well as the results of some protypes manufactured to reduce the project risk.