A recently proposed model for the class of stellar objects known as eruptive symbiotic systems, consists of a binary system containing a cool, mass-losing giant and a hot, compact companion which erupts with a wind of its own. The structure and time development of the nebula which forms at the interface of the two stellar winds has been studied with the aid of two different numerical formulations. The first describes the roughly conical portion of the nebula which reaches a steady state configuration. The second describes the formation and time development of the entire nebula, in a less rigorous formulation, which does, however, include the effects of the stars' orbital motion. Both formulations approximate the nebula as a zero-thickness shell. It is argued that this restricts the use of the numerical models to systems which radiate away the energy of the winds which continually collide with the nebula;Results of the steady state formulation are used to relate the shape and internal velocity and mass density distributions within the conical portion of the nebula, to two parameters, m and w, which are the ratio of the mass loss rates and the ratio of the velocities of the two stellar winds. The shell structures which result from a range of values of m and w are tabulated;Finally, using geometrical information, previously deduced from observations for the eruptive symbiotic V1016 Cyg, it has been possible to place rough limits on the value of the product of the parameters, mw, for this system.