A layering algorithm for flat modular origami models is presented. The need for drawing models automatically generated by a computer program was the driving force for this work. The three issues are discussed: (i) how to represent a modular form, (ii) how to provide information about locking of modules, and (iii) how to generate the layering for a model. While the algorithm was developed independently, the core part of it is equivalent to the Flat Folder developed by Ku (Jason S. Ku, Flatfolder main page.) for single-sheet origami models. The main difference is that instead of a graph proposed by J. Ku, the specific configurations of the folded form are translated into a set of logical clauses of 0 order, and the layering is generated by a simple inference system. The Flat Folder aims to find all possible variants of layering for a single-sheet origami, while drawing a modular form was the rationale of this article. That resulted in another approach to the problem: resolving certain ambiguity of layering is a part of the design. In the same way, the position of crease lines in the CP is a part of the design process. So the algorithm takes as input data not only CP and the folded form of a model, but also a partial specification of layering, especially for flaps in pockets of joined modules. Such an approach avoids the exponential complexity of the algorithm, and the layering is generated in polynomial time. The algorithm is structured for better performance in two ways. First, the part of lower numerical complexity is applied, then if it fails, a part of higher complexity is applied, and the partial results improve its performance. Second, in the typical case of identical modules, the layering problem for the complete model may be decomposed into layering of a single module, next replicated for all modules, and followed by layering the overlapping parts of different modules. Finally, the numerical issues generating false results for testing the geometric structure of the folded form are discussed and solved by the application of “geometry of fat lines.”