The paper presents a new method for computations of the magnitude and phase envelopes of uncertain transfer functions. The idea is to factor the transfer function into its real and complex pair roots and find the maximum and the minimum magnitudes of the gain and phase of each factor. The Bode envelopes of the given uncertain system are then found from those of the individual factors. This approach, which is different from those based on the interval polynomial method of Kharitonov, has the major advantage that the representation is more applicable to practical situations where typically the coefficients of the various factored terms relate to physical parameters of a mathematical model. Further the method results in narrower envelopes and therefore improved designs as illustrated in the examples which consider, lead, PI and PID controller designs.