We have conducted two-dimensional hydrodynamic simulations of the mass transfer of the short-period binary Algol (beta Persei). Optical H alpha line observations suggest that the Algol system possesses a transient accretion disk, in contrast to long-period systems in which a steady accretion disk is inferred. We have used our model to explore the dependence of the circumstellar flow on three parameters: the velocity, angle, and density of the tidal stream of gas flowing from the evolved companion star toward the more massive main-sequence star. The flow is relatively insensitive to the initial speed and direction of the tidal stream, but varies substantially depending on the density of the stream. For high values of the stream density, n(sub s) is greater than or approximately 10(exp 9)/cu cm, the gas is effectively isothermal and does not bounce off the surface of the primary star. For low values of the stream density, n(sub s) is less than or approximately 10(exp 8)/cu cm, the gas is effectively adiabatic and the high thermal pressure generated when the stream strikes the stellar results in an extended accretion disk. In the intermediate range of stream density, radiative cooling is only partially effective, and the tidal stream produces a variable accretion disk reminiscent of the transient accretion disk suggested by the optical observations. In all of our simulations the region of highest thermal pressure corresponded to the region of interaction between the gas stream from the secondary and the gas which had circled the primary star. This interaction region near the surface of the primary star at the line of centers may be the source of the localized H alpha emission observed in Algol.