In mammals and invertebrates the proliferation of an invading transposable element (TE) is thought to be stopped by an insertion into a piRNA cluster. Here we explore the dynamics of TE invasions under this trap model using computer simulations. We found that piRNA clusters confer a substantial benefit, effectively preventing extinction of host populations from a proliferation of deleterious TEs. TE invasions consists of three distinct phases: first the TE amplifies within the population, next TE proliferation is stopped by segregating cluster insertions and finally the TE is inactivated by fixation of a cluster insertion. Suppression by segregating cluster insertions is unstable and bursts of TE activity may yet occur. The transposition rate and the population size mostly influence the length of the phases but not the amount of TEs accumulating during an invasion. Solely the size of piRNA clusters was identified as a major factor influencing TE abundance. We found that a single non-recombining cluster is more efficient in stopping invasions than clusters distributed over several chromosomes. Recombination among cluster sites makes it necessary that each diploid carries, on the average, four cluster insertions to stop an invasion. Surprisingly, negative selection in a model with piRNA clusters can lead to a novel equilibrium state, where TE copy numbers remain stable despite only some individuals in a population carrying a cluster insertion. In Drosophila melanogaster the trap model accounts for the abundance of TEs produced in the germline but fails to predict the abundance of TEs produced in the soma.