Polymeric membranes have gained popularity as fibrous structures for tissue regeneration. This research focuses on the rotary jet spinning (RJS) process combined with a polymer as a strategy for designing membranes. To this end, RJS‐polyurethane (RJS‐PU) membranes with different microstructures were produced. Considering the effects of solution properties on fiber production, the viscosity of PU solutions was evaluated. Membrane morphology was studied based on scanning electron microscopy and 2D fast Fourier transform analysis. The chemical and thermal properties were characterized by Fourier‐transform infrared spectroscopy and thermogravimetric analysis, respectively. 3‐(4,5‐Dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide and Live/Dead cell assays were performed to determine the material cytotoxicity by assessment of the profile of proliferation and cell viability. The results indicated that the combination of PU and RJS was an effective one for the production of fibrous structures for tissue engineering applications, demonstrating good compatibility with the cultured osteoblastic cell line. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48455.