The development of integrated applied software environment for mathematical modelling, which is oriented onto solving interdiscipline direct and inverse problems by the wide circle of users in the framework of cloud computing at the supercomputers of petaflops level stands the big set of issues of methodical, technological and organizational types. In this paper, we consider the conception of basic system of modelling (BSM), whose functionality is supposed in the framework of collective using computing center (CUCC). BSM presents the integrated software environment which supports all main technological stages of large scale computational experiments, adapted to evolution of the problem models and algorithms, as well as to architectures of multi-processor computational systems (MCS), and intended to the long life circle, which is provided by the efficient constructing of applied program packages (APPs). The achivement of the total high performance of CUCC is considered as the constrained optimization problem for the schedule of computational tasks, under taking into account the necessary resourses for the particular applications.