The paper is focused on the interface design patterns for interactive modeling and it is an effort to systematically describe the usage of UID patterns in this area. Main objectives were to develop the UID patterns to increase the usability of the software for numerical computing and to make the process of numerical simulation highly interactive. On the basis of these UID patterns authors developed reusable software components in several programming languages: Java, Python, C++ and Matlab. The patterns described in the paper were verified in the development of practical software tools for demographers and biostatisticians, but can be readily applicable to other domains of numerical computing.