  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 SDSS and Spitzer IRAC 3.6 $\mu$m 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.
