Abstract: In order to get the analytic algorithm for the indexes of two-stage start-up demon-stration test models, a Markov chain which satisfies the state transition rules of the two-stage start-up demonstration test models was constructed. The matrix formulas of the expected value, variance, probability mass function, distribution function of the test length, and the probability of rejection and acceptance were given using Markov chain theory. Numerical examples indicate that the finite Markov chain imbedding approach is more effective than probability generation function in evaluating the various indexes of two-stage start-up demon-stration test models with all kinds of parameters.