The article provides an analysis of modern and affordable software systems for modelling shells of complex geometry and the possibilities of using these software systems in 3D printing. Such an analysis made it possible to choose software systems that most accurately allow for the implementation of the 3D modeling method proposed in the article with subsequent printing on a 3D printer. This method is considered in detail on the example of constructing several types of helicoids. The process of 3D modeling of a helicoid is described step by step and is divided into several stages: parametric modeling of a helicoid in SCAD, editing of the resulting model in AutoCAD and its export to a special format for 3D printing. The use of the method of parametric modeling is due to its accuracy and uncompromisingness. With its help, one can accurately judge the type of the built surface. Parametric modeling is the construction of a surface by compiling equations on each axis, i.e. along the x, y, z axes, and for each type of surface there are specific characteristic equations. It is not possible to implement the method of parametric modeling in all software systems; in this connection, certain difficulties arise. The article analyzes the difficulties encountered in 3D modeling of the helicoid and suggests ways to solve them.