The article offers an extended mathematical model for estimating the optimal number of computing nodes in a private university cloud using virtual workstations (VDI), and taking into account the information security requirements of a cloud-based learning environment (OSS) of universities. Unlike previously known approaches, the developed model takes into account not only the resource load (CPU, RAM), but also the requirements for the security level of virtual machines and servers. In the proposed model, quantitative parameters of the security of the OSS are introduced, and the task of VM deployment is reduced to a multi-criteria optimization balancing between resource efficiency and compliance with the security requirements of the OSS. A simulation simulation of the cloud operation with typical parameters of the university IT infrastructure has been carried out, confirming the practical significance of the proposed approach. The model is suitable for designing secure cloud platforms in the educational environment of universities of the Republic of Kazakhstan.