Vector-borne disease control using transgenic mosquitoes requires transgene spread to high frequency in populations. Transposable elements (TE's) are genetic entities that replicate within the genome of other organisms. Replication gives TE's an inheritance advantage in the next generation and allows them to spread through populations in spite of fitness costs. TE spread can theoretically drive linked transgenes into populations. Current models of TE dynamics do not take into account TE post-integration behavior or dynamics of TE copy number. We created a simulation model to examine the impact of these factors on TE spread in mosquito populations. The model parameters are: 1) transposition rate/insert/generation, 2) fitness cost/insert, 3) rate of inter vs. intrachromosomal movement, and 4) recombination rate between adjacent inserts. If TE's induce no fitness costs, they will spread over a wide range of parameter values but spread is slower for less ideal rates of transposition, recombination and inter vs. intrachromosomal movement. If TE's induce fitness costs, high rates of intrachromosomal movement can halt the spread of elements, or cause them to take an unacceptably long time to spread. Simulations indicate that TE's with ideal transgene drive characteristics will transpose ≥10%/insert/generation, induce ≤1% fitness cost/insert, and move preferentially to unlinked sites in the genome. Current mosquito TE's do not meet these requirements. Our results suggest that before TE's can be used as transgene drivers in mosquito populations, 1) better TE's must be identified or engineered and 2) more complex models that include critical aspects of TE biology must be further developed.