We propose a new approach to the 3D layout problems based on the integration of constraint programming and virtual reality interaction techniques. Our method uses an open-source constraint solver integrated in a popular 3D game engine. We designed multimodal interaction techniques for the system, based on gesture and voice input. We conducted a user study with an interactive task of laying out room furniture to compare and evaluate the mono- and multimodal interaction techniques. Results showed that voice command provided the best performance and was most preferred by participants, based on the analysis of both objective and subjective data. Results also revealed that there was no significant difference between the voice and multimodal input (voice and gesture). Our original approach opens the way to multidisciplinary theoretical work and promotes the development of high-level applications for the VR applications.