We present a detailed photometric study of a sample of 22 edge-on galaxies with clearly visible X-shaped structures. We propose a novel method to derive geometrical parameters of these features, along with the parameters of their host galaxies based on the multi-component photometric decomposition of galactic images. To include the X-shaped structure into our photometric model, we use the IMFIT package, in which we implement a new component describing the X-shaped structure. This method is applied for a sample of galaxies with available Sloan Digital Sky Survey and Spitzer IRAC 3.6 µm observations. In order to explain our results, we perform realistic N-body simulations of a Milky Way-type galaxy and compare the observed and the model X-shaped structures. Our main conclusions are as follows: (1) galaxies with strong X-shaped structures reside in approximately the same local environments as field galaxies; (2) the characteristic size of the X-shaped structures is about 2/3 of the bar size; (3) there is a correlation between the X-shaped structure size and its observed flatness: the larger structures are more flattened; (4) our N-body simulations qualitatively confirm the observational results and support the bar-driven scenario for the X-shaped structure formation.