Accurate prediction of shellside pressure drop in a baffled shell-and-tube heat exchanger is very difficult because of the complicated shellside geometry. Ideally, all the shellside fluid should be alternately deflected across the tube bundle as it traverses from inlet to outlet. In practice, up to 60% of the shellside fluid may bypass the tube bundle or leak through the baffles. This short-circuiting of the main flow reduces the efficiency of the exchanger. Of the various shellside methods, it is shown that only the multi-stream methods, which attempt to obtain the shellside flow distribution, predict the ~ressure drop with any degree of accuracy, the various predictions ranging from -30% to +70%, generally overpredicting. It is shown that the inaccuracies are mainly due to the manner in which baffle leakage is modelled. The present multi-stream methods do not allow for interactions of the various flowstreams, and yet is is shown that three main effects are identified, a) there is a strong interaction between the main cross flow and the baffle leakage streams, enhancing the crossflow pressure drop, b) there is a further short-circuit not considered previously i.e. leakage in the window, and c) the cross flow does not penetrate as far, on average, as previously supposed. Models are developed for each of these three effects, along with a new windowflow pressure drop model, and it is shown that the effect of baffle leakage in the window is the most significant. These models developed to allow for various interactions, lead to an improved multi-stream method, named the "STREAM-INTERACTION" method. The overall method is shown to be consistently more iccurate than previous methods, with virtually all the available shellside data being predicted to within ±30% and over 60% being within ±20%. The method is, thus, strongly recommended for use as a design method.