Using a two-pool exchange model of magnetization transfer (MT), numeric simulations were developed to predict the time dependence of longitudinal magnetization in both semisolid and liquid pools for arbitrary pulsed radiofrequency (RF) irradiation. Whereas RF excitation of the liquid pool was modeled using the time-dependent Bloch equations, RF saturation of the semisolid pool was described by a time-dependent rate proportional to both the absorption lineshape of the semisolid pool and the square of the RF pulse amplitude. Simulations show good agreement with experimental results for a 4% agar gel aqueous system in which the two-pool kinetics have been well studied previously. These simulations provide a method for interpreting pulsed MT effects, are easily extended to biologic tissues, and provide a basis for optimizing clinical imaging applications that exploit MT contrast.