The present note follows the previous one, part I, where theoretical tools for analyzing structures made by no-tension (NT) material are presented in extensive form. Some significant results are presented in this part II of the note, ranging from the highlight of problems related to the treatment of singularities possibly occurring in the modeling of loads that burden on NT structures, and the development of tools for their treatment, to the specialization of general problems to planar and spatial structures, with the related ad hoc conceived analytical set up, original numerical tools, and noncommercial software. The implementation of the problems, deriving from the set up of the constrained optimization presented in part I of the note, is developed together with a number of applications, also providing, in some cases, the comparison of numerical, experimental, and/or field evidence referred to masonry structures, which finally validates the applicability of the adopted approach for the analysis of masonry constructions.