We discuss the role of the local interstellar magnetic field on the interaction of the solar wind with the local interstellar medium (LISM). In particular, we consider the case in which the LISM flow is aligned with the magnetic field. The solar wind inside the termination shock is spherically symmetric, and the LISM magnetic field varies between 0.0 and 3.5 ¿G. Our simulations show that for the case of field-aligned flow, increasing the interstellar magnetic field intensity Bis moves the bow shock (when it exists) and heliopause further outward from the Sun. This effect is explained in terms of the $vec{J} times vec{B}$ force on the plasma. We compare our results with comparable simulations carried out by Aleksashov et al. <2000>. The comparison leads to the conclusion that the mutual dependence between the neutral hydrogen number density and the strength of the magnetic field characterizes the solution for the interaction between the solar wind and interstellar medium. For a given interstellar neutral hydrogen number density (assumed to be available with present observations, or more exactly obtained from future observations), and for a given LISM magnetic field direction and intensity, the model gives distances to the heliopause and the termination shock, and the flow structure ahead of the heliopause. Thus the model can be used to estimate the LISM magnetic field intensity consistent with the observations.