The conceptual design stage often involves a compound set of objectives and constraints such as abstract notions of function and aesthetic, performance, project requirements, site constraints, and construction costs. To respond to these complexities, a number of design instances and alternatives need to be developed and assessed against predefined criteria. While this process requires human imagination, computational generative systems are increasingly being used in this stage of the design process. However, some of these approaches have limitations in the ability to make modifications within an interactive environment, requiring a model to be recreated with different attributes and parameters if changing geometry configuration or topology are needed. This research introduces a new approach - Parametric Design Procedures (PDPs) - which combines the techniques of Design Procedures and Parametric Modeling to address the limitations of existing systems. PDPs offer possibilities to explore a particular design instance after a model is constrained through the generation of an infinite number of design instances which can be considered in the evolution of parametric design instances. The rationale for and features of PDPs are described. The viability of this approach is explored through a prototype implementation in Grasshopper. The brief for an architectural design competition is used as the basis for the prototype development. The paper concludes with suggestions for further research and development, for example in the use of other software and other design phases to test the implementation and viability of PDPs.