This paper summarizes the numerical results obtained by three‐dimensional MHD simulations of the interaction between the solar wind and interstellar medium inRatkiewicz and Ben‐Jaffel[2002],Ratkiewicz and McKenzie[2002], andRatkiewicz and Webb[2002]. We analyze the configuration in which Maxwell stresses lead to squeezing and/or pushing the heliospheric boundary. In particular, we explain the mechanism giving rise to a suction effect of the heliopause. Numerical results for the case of aligned interstellar MHD flow are compared with previous studies. © 2003 American Institute of Physics