Development of convection in sun's outer shell is caused by reduction of effectiveness of energy transfer by radiation. Traditionally, models of solar convection are considered to be axisymmetric on the scale of solar radius. Such models provide basic understanding of convection under solar conditions. However, interpretation of a number of observable large-scale long-lived solar phenomena requires developing a non-axisymmetric approach. We present such a model in which large-scale non-axisymmetry is caused by large-scale flows such as Rossby waves and vortices. We model flows near the base of the solar convection zone. Anelastic approximation is used, which is valid for flow velocities much smaller than local sound speed. Our three-dimensional numerical simulations show that interaction of convection with large-scale flows leads to the establishment of non-axisymmetric large-scale temperature distribution. The interaction also gives rise to large-scale variations of penetration depth of convective plumes. Generation of the magnetic field by large-scale non-axisymmetric flows can explain such solar phenomena as complexes of activity, active longitudes, drifts of large-scale magnetic fields from equator to the poles, and appearance of distinct rotation periods of magnetic fields at some latitudes. We discuss a possibility of detection of large-scale non-axisymmetric flows and temperature distributions associated with them by the methods of helioseismology.