The Brazilian Justice Power has been flooded by a wave of lawsuits related to the fundamental right of health, facing, recently, a problem of great constitutional repercussion, which is the obligatorily of high cost medicine supplyment by the State, over which will be decided the new paths for Brazilian public health, especially in regards to the reach of the principles of wholeness. In an attempt to distribute the heavy cost of supliment of high cost medicine, some States are using the calling to the process of the other federate agents to integrate the whole, which hasn t been permitted in the jurisprudence, over the argument of being a mere proselyting tool. In this factual and juridical context, the present dissertation is done in three chapters, to analyze, at first, the public health in Brazil, in the second, the matter of the judge mentation of the suppliment of high cost medicines to the State; and, in third, the admissibility of the calling to the process in these demands. The study is based in the statistic data research related to the lawsuits involving the right to health, supported, also, in the analysis of concrete cases, which proves the academicals, political, economic and social importance of the subject, keeping in mind the speeches regarding the material possibilities of the State in the effective and satisfactory availability of health rights to the population. This final chapter is dedicated to the demonstration of the availability of the calling to the process of the other agents co-obligated in solidarity, for the distribution of the cost for the suppliment of high cost medicine, as an instrument of effectuating, not just the legal lawsuit, as well as the constitutional right of social solidarity.