The aim of this study is the construction and preparation for the practical use of mathematical models of multivariate calculus problems on quadrature parabolas. Objectives of the study is to construct mathematical models of multivariate calculus problems on areas parabolic shapes and develop software for their automated generation. The object of research is build process problems in calculating the area of parabolic shapes. The subject of research is mathematical model of multivariate calculus problems on areas parabolic shapes and software automation of their generation. The paper presents the stages of constructing mathematical models of multivariate calculus problems on areas parabolic shapes. The modeling is based on the use of a square with parameter a. Diagonal vertices of a square is the point (0; 0) and (a; a) inscribed in a square parabola passing through three given points; the coordinates of the points derived equation and the parabola formula for calculating the area of a parabolic shape, bounded by sides and a square parabola. By providing a setting different values have a multiple tasks. For teachers proposed a program generator problems that implemented among SageMathCloud. Results of the study identified areas for further authors research in modeling and generation systems, problems with school courses, elementary and higher mathematics.