Let Z(t) be a stationary centered Gaussian process with a Markovian structure. In some fluid models, the stationary buffer content V can be expressed as sup t$0 ð R t 0 ZðsÞ ds 2 ctÞ and PðV . uÞ ¼ Ce 2gu ð1 þ oð1ÞÞ: The asymptotic constant C can be expressed by the so called generalized Pickands constants H . In most cases no formula or approximation for C are known. In this paper we show a method of simulation of C by the use of change of measure technique. The method is applicable when Z(t) is a stationary Ornstein-Uhlenbeck process or ZðtÞ ¼ P n j¼1 X j ðtÞ; where ðX 1 ðtÞ; . . .; X n ðtÞÞ is a Gauss-Markov process. Two examples of simulations are included. Moreover we give a formula for a lower bound for generalized Pickands constants.