We simulate the three-dimensional structure of the heliosphere during solar activity minimum by specifying boundary conditions at the coronal base. We compare the output of the model with Ulysses observations obtained during the spacecraft's first fast latitude transition in 1994--1995. The polytropic MHD equations are solved for a steady coronal outflow that includes the addition of Alfv¿n wave momentum and energy in the WKB approximation. A solution for the outflow in a tilted dipole magnetic field in the inner computational region (1--20 R⊙) is combined with a three-dimensional solution in the outer region which extends to 10 AU. The inner region solution is essentially the same as in the work of Usmanov et al. <2000> but has been obtained for slightly different boundary conditions using a different numerical algorithm. The dipole orientation is chosen to match the one inferred from photospheric magnetic field observations at the Wilcox Solar Observatory. The steady solution in the outer region is constructed using a marching-along-radius method and models both solar rotation and interaction regions. The bimodality of solar wind with a rapid change in flow parameters with latitude and the observed extent of the slower wind belt are reproduced well. We compare our simulation also with the results of Bruno et al. <1986> and empirical models of coronal density. We show that the simulation results are in good agreement with the empirical model of Wang and Sheeley <1990>.