A report on the workshop Computational mechanics of generalized continua and applications to materials with microstructure (Catania 29–31 October 2015) is provided. The constructive atmosphere that was present at the workshop in 2012 and the Euromech Colloquium in 2014, both in Cisterna di Latina, was repeated for this workshop in Catania. The objective of this meeting was to bring together experts within the CNRS International Associate Laboratory (LIA) Francois Cosserat–Tullio Levi Civita Coss & Vita in order to discuss topics of common interest. Particularly, the workshop was dedicated to the following projects of LIA: (i) computational mechanics of generalized continua; and (ii) nonlinearity and stability in continuous media. Also subjects related to the application of generalized continua to multiscale and smart materials were discussed. Approximately 25 Coss & Vita LIA members and other experts (mostly from France and Italy) gathered together, including PhD students and those students from the Scuola Superiore di Catania.