The phase problem is one of the major problems in crystallography. In the absence of phase information, a variety of electron density distributions is consistent with the observed magnitudes. This ambiguity may be reduced significantly if the distribution values are restricted to 0 or 1 values, i.e. when the object of search is an envelope rather than a continuous electron density distribution. The density values are linked to the observed magnitudes and unknown phases by a system of non­linear equations. We present a method to replace these equations by a system of linear inequalities. As a consequence, powerful tools of integer linear programming may be applied to solve the phase problem. This novel approach was tested on calculated and experimental data for a known protein structure. At the moment, the size of the grid for the envelope calculation is the major limitation of the approach. Nevertheless, even for a very small grid, some structure information can be extracted and used as a starting point for further phase improvement or as a way to solve the molecular replacement problem.