Research data and code supporting the paper ""Mesoscale modeling of deformations and defects in thin crystalline sheets"". Code (apfc-python-surf.zip) The implementation of the APFC model is performed in python by exploiting the pseudo-spectral Fourier method. Library pyfftw is adopted. However, standard fft libraries can be used as well by changing the corresponding module/functions. The code supports equations of the APFC model both coupling with the evolution of the surface considered in this work and on a simple flat domain. Updates can be found in the GitLab repository linked below. GitLab repository for the code https://gitlab.com/3ms-group/apfc_python/ Data The data.zip files contain the simulation results and auxiliary scripts used to produce the results illustrated in the paper's figures. The folder numbering refers to the one used for the figures in the final version. For further information please contact the authors.