This paper provides a detailed description of the latest version of our model of the solar wind (SW) interaction with the local interstellar medium (LISM). This model has already been applied to the analysis of Lyman-alpha absorption spectra toward nearby stars and for analyses of Solar and Heliospheric Observatory/SWAN data. Katushkina et al. (this issue) used the model results to analyze IBEX-Lo data. At the same time, the details of this model have not yet been pub-lished. This is a three-dimensional (3D) kinetic-magnetohydrodynamical (MHD) model that takes into account SW and interstellar plasmas (including α particles in SW and helium ions in LISM), the solar and interstellar magnetic fields, and the interstellar hydrogen atoms. The latitudinal dependence of SW and the actual flow direction of the interstellar gas with respect to the Sun are also taken into account in the model. It was very essential that our numerical code had been developed in such a way that any numerical diffusion or reconnection across the heliopause had not been allowed in the model. The heliospheric current sheet is a rotational discontinuity in the ideal MHD and can be treated kinematically. In the paper, we focus in particular on the effects of the heliospheric magnetic field and on the heliolatitudinal dependence of SW. Subject headings: Sun: heliosphere 1. Introduction Global modeling of the solar wind (SW) interaction with the local interstellar medium (LISM) is essential: (1) in general, to understand how the Sun acts as a star and exchanges matter and energy with the LISM, and (2) in particular, to explain relevant space experiment data (e.g. obtained on board of both Voyager spacecraft, the Interstellar Boundary Explorer (IBEX), the Solar and Heliospheric Observatory (SOHO), the Hubble Space Telescope (HST), etc.).Following the pioneering paper by Baranov & Malama (1993) self-consistent kinetic-gas dynamics models of the SW/LISM interaction were developed by our group in Moscow (e.g. Izmodenov and Baranov, 2006, Izmodenov et al., 2009, for reviews). There are two features which make our model approach different from similar models developed by other groups. These features are as follow: (1) a rigorous kinetic treatment of the interstellar H atom component using a Monte Carlo method with splitting of the trajectories, and (2) a Godunov-type numerical method used to solve the ideal gas dynamical or MHD equations. The method has the potential to fit some major discontinuities of the flow and to capture the others. The kinetic treatment of H atoms is essential because their mean free path is comparable to the size of the SW/LISM interaction region (see, e.g.,Izmodenov 2000). The difference between kinetic and alternative multi-component models has been explored in detail by Alexashov & Izmodenov (2005) and Müller et al. (2008). At the heliospheric distances smaller than 10-20 AU, solar gravitation and radiation forces make the kinetic effects even more important. The velocity distribution function of H atoms is essentially non-Max...