The growth and spread of new polyploid populations have been explained in terms of fitness advantages over their diploid progenitors. However, a fitness advantage is not sufficient to insure the establishment of a polyploid; it must also overcome the obstacles of demographic stochasticity and minority disadvantage. Several studies have addressed the population dynamics of autopolyploids, but the present study is the first to consider allopolyploids, which are affected by more factors than autopolyploids. We constructed a population dynamic model of four types of plants (two parent species, hybrids, allopolyploids) that also included an explicit breeding system. The numbers of plants of each type were the most important factors determining whether the new allopolyploid would become established. More polyploid plants greatly increased the likelihood of polyploid persistence. More plants of the parent species and more hybrids resulted in more polyploids being produced. The model parameters with the most effect on polyploid establishment were potential population size (K), individual plant fecundity, and niche separation (α). The most important breeding system parameters were selfing rates, which mitigated minority disadvantage imposed by pollen limitation. The importance of population sizes, and the parameters that controlled them, in overcoming demographic stochasticity parallels the well-recognized role of propagule pressure in determining the success of invasive species. We modeled the establishment of a new allopolyploid; analogous considerations would affect the establishment of a new autopolyploid. The critical role of population sizes in polyploid establishment should be more widely recognized.