The evolution of short repeated sequences by replication slippage under the assumption of selective neutrality is modeled using a linear birth and death process. The equilibrium distribution, the distribution of the life expectancy of a repeated sequence when the process starts from two repeats, the age distribution of repeats, the probability of obtaining two genes with i and j copies which diverged t generations ago and the conditional variance of copy number given the repeat number is more than one are computed. The distributions of life expectancy and age are shown to have long tails. Also the statistic which estimates the conditional variance is shown to have a large coefficient of variation. Using these theoretical results, we develop an approximate test of our model and analyze persistent repeated sequences found in the primate beta-globin gene region and Oenothera chloroplast DNA which are polymorphic within species. We found one sequence in Oenothera chloroplast DNA which does not fit to our neutral model.