A model is developed to estimate the passage time of a block of data through a group of tandem buffered switches of a buffered data network. In particular, the first two moments and the distribution function of this block passage time are estimated. This estimation procedure contains many assumptions and heuristic arguments that are based on the author's intuition and/or experience. Simulation results of the block passage time through a sample buffered network are presented and are compared with the results of the estimation procedure. The delay performance of this example buffered network is also studied by making a delay comparison between the sample buffered network and a point-to-point private-line arrangement.