The free vibrations of a wide range of tapered rectangular plates with an arbitrary number of intermediate line supports in one or two directions are investigated[ The domain of the plate is bounded by x aa\ a"9 ΒΎ a Β³ 0# and y bb\ b"9 ΒΎ b Β³ 0# in the rectangular co!ordinates[ The thickness of the plate is con! tinuously varying and proportional to a power function x s y t [ A variety of tapered rectangular plates can be described by giving the taper factors s and t various values[ The intermediate line supports run parallel to the edges of the plate[ A new set of admissible functions\ which are the static solutions of the tapered beam with intermediate point supports\ or a strip taken from the plate structure in one or the other direction under a Taylor series of loads\ is developed[ Consistent convergency independent of the truncation factors a and b of the plate can be obtained by taking the midpoint of the beam as the expanding point of the Taylor series[ Unlike conventional admissible functions\ this set of static beam functions can appropriately vary with the thickness variation of the plate[ The eigenfrequency equation of the plate is derived by the RayleighΓRitz approach[ A general computer program has been compiled[ It can be seen that the convergency of the numerical computation is very rapid and that the _rst few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions[ Sets of _rst!time reported eigenfrequency data are included for future reference[