The absence of constraints is one of the major limitations in current Virtual Reality (VR) environments. Without constraints, it is difficult to perform precise 3D interactive manipulations in VR environments and precise solid modelling in VR environments cannot be guaranteed. In this paper, constraints are incorporated into the VR environment for intuitive and precise solid modelling. A hierarchically structured constraint-based data model is developed to support solid modelling in the VR environment. Solid modelling in the VR environment is precisely performed in an intuitive manner through constraint-based manipulations. Constraint-based manipulations are accompanied with automatic constraint recognition and precise constraint satisfaction to establish the hierarchically structured constraint-based data model and are realized by allowable motions for precise 3D interactions in the VR environment. The allowable motions are represented as a mathematical matrix for conveniently deriving allowable motions from constraints. A procedure-based degree-of-freedom incorporation approach for 3D constraint solving is presented for deriving the allowable motions. A rule-based constraint recognition engine is developed for both constraint-based manipulations and implicitly incorporating constraints into the VR environment. A prototype system has been implemented for precise solid modelling in an intuitive manner through constraint-based manipulations in the VR environment.