Vacuum tube amplifiers, known for their acclaimed distortion characteristics, are still widely used in hi-fi audio devices. However, bulky, fragile and power-consuming vacuum tube devices have also motivated much research on digital emulation of vacuum tube amplifier behaviors. Recent studies on Wave Digital Filters (WDF) have made possible the modeling of multi-stage vacuum tube amplifiers within single WDF SPQR trees. Our research combines the latest progress on WDF with the modified blockwise method to reduce the overall computational complexity of modeling cascaded vacuum tube amplifiers by decomposing the whole circuit into several small stages containing only two adjacent triodes. Certain performance optimization methods are discussed and applied in the eventual real-time implementation.