The paper contributes to the shape grammars based formal design theory by first providing a formal definition of shape rules and shape rule algebras, and then utilizing this new tools to: construct new shape rules from the old ones, define meta shape grammars that generate new shape grammars by modifying the rules of the existing ones, provide a formal representation of Stiny’s rule schemas which allows for their manipulation, define a shape rule decomposition as a set of shape rules that sums to a shape rule, and analyze calculations with shapes via shape rule decompositions.