In this thesis, we will be studying the short-maturity asymptotic analysis of American put option in a so-called multifactor model introduced by Medvedev and Scaillet (2009). In such a multifactor model, the underlying stock price is assumed to follow the same stochastic process as in the classical Black-Scholes model. In addition, the volatility and interest rates are not constant any more, they are also assumed to follow some stochastic processes. In Medvedev & Scaillet (2009), a short-maturity asymptotic analysis of American put price in the multifactor model has been carried out and a general formula for the asymptotic expansion of price is given. However, the explicit formula for the coefficients in the expansion is not provided. In this thesis, we examine and extend the asymptotic analysis done by the aforementioned scholars and determine the coefficients of the expansion. The main result of the thesis is a 2nd order asymptotic expansion for the American put with the explicit formula for the coefficients given.