This note deals with the problem of computing the frequency response of an uncertain transfer function whose numerator and denominator polynomials are multiples of independent uncertain polynomials of the form P(s, q) = l(0) (q) + l(1) (q) s + ... + l(n) (q) s(n) whose coefficients depend linearly on q = [q(1), q(2),...,q(q)](T) and the uncertainty box is Q = {q: q(i) is an element of [q(i), q(i)], i = 1, 2,..,q}. Using the geometric structure of the value set-of P(s, cl), a powerful edge elimination procedure is proposed for computing the Bode, Nyquist, and Nichols envelopes of these uncertain systems. A numerical example is included to illustrate the benefit of the method presented.