The interaction of the heliosphere with interstellar clouds has attracted interest since the late 1920’s, both with a view to explaining apparent quasi-periodic climate “catastrophes” as well as periodic mass extinctions. Until recently, however, models describing the solar wind - local interstellar medium (LISM) interaction self-consistently had not been developed. Here, we describe the results of a two-dimensional (2D) simulation of the interaction between the heliosphere and an interstellar cloud with the same properties as currently, except that theH0density is increased from the current value ofn(H0)∼0.2 cm−3to 10 cm−3. The mutual interaction of interstellar neutral hydrogen and plasma is included. The high density neutral interstellar cloud leads to a considerable reduction in the size of the heliosphere (approximately 9 - 14 AU to the termination shock in the upstream direction) and is highly dynamical. The interplanetary environment at the orbit of the earth changes markedly, with the density of neutral H increasing to ∼2 cm−3. The termination shock forms, disappears, and reforms periodically, and mixing of the shocked/subsonic solar wind and the LISM plasma occurs due to the presence of ion-neutral friction driven instabilities in the vicinity of the heliospheric nose. ©1999 American Institute of Physics.