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A method for analysing tapered lossy transmission lines is presented. The telegrapher's equations are solved by using the closed-form Green's function of the corresponding uniform transmission line. The space-dependent characteristic impedance is handled as a forcing term of the telegrapher's equations whose effect is incorporated into the Fredholm integral equation of the second kind describing the space voltage distribution. The method allows to avoid the segmentation technique which is prone to inaccuracies because of spurious reflections at the boundaries of each section. Several tests are carried out and excellent results are obtained confirming the superior accuracy of the proposed method with respect to the standard segmentation technique.