A model for calculating the viscous flow of steam through a conical perforated steam sieve is proposed. The model takes into account the complex geometry of the channels, the results of design and engineering developments and computational studies to optimize the stop valves of the steam line for flow path of the high-pressure cylinder of the K-220-44-2 turbine for the Loviisa NPP are considered (Finland). The main attention during the modernization of stop valves 1 and 2 was paid to the problem of reducing losses on the steam sieve. A number of design features largely offset the effect of a large number of holes. These include the flow around the perforated surface at an angle to the axis of the holes; obstruction of the steam line channel behind the side surface of the steam sieve with three longitudinal ribs, as well as by an annular zone without holes at the junction of the side and bottom surfaces. During modernization the inner diameter of the inlet part of the body in casting was increased, which made it possible to increase the free cross-section of the perforated steam sieve. The proposed design solutions were investigated numerically. The spatial three-dimensional flow of a viscous compressible steam through the flow path was analyzed by numerically integrating the system of Navier-Stokes equations averaged by Reynolds-Favre. The system was supplemented with equations of the differential turbulence model. The integration of the system of Navier-Stokes equations and associated equations was carried out using the author's software package. The calculated subdomains were approximated by unstructured hexahedral meshes. The solver used an implicit difference scheme of finite volumes of the 2nd order of accuracy and a variant of the algorithm that allows efficient splitting of the computational process for multiprocessor platforms. The solid walls were assumed to be adiabatic, the no-slip condition and the equality of effective vortex viscosity to zero were set on them. Turbulent effects were described based on the Menter model and the modified Spalart-Allmaras turbulence model.