The paper presents a theory of capacitor bushings for both infinite and finite numbers of foils. Two bushing contours are considered, namely the straight-line contour and the contour which gives uniform axial potential gradient. The general line followed is to determine for each contour (a) the radial stress in the insulating material, (b) the location of the place of minimum radial stress, (c) the flange radius, and (d) the minimum flange radius.Consideration is given to the case where the conductor radius is fixed, and also to the important practical case where the length of the earth flange is fixed.The theory of capacitor bushings has been well covered by previous publications for the case of an infinite number of foils. The present paper extends this previous work, particularly in respect of the method of locating the position and magnitude of the minimum radial stress. The published theory of capacitor bushings is meagre for the case of a finite number of foils. The present paper covers new ground in the following: (a) the theory of a bushing with straight-line contour; (b) the location and magnitude of the minimum radial stress; (c) the theory when the limiting stress is that occurring at the last foil but one, instead of at the last foil.Throughout the paper the method of determining minimum flange radius differs substantially from that given previously. Since for each contour the cases of infinite and finite numbers of foils are considered, this permits of a determination of the error made if results obtained for an infinite number of foils are used when the number of foils is finite.The paper does not include the bushing theory for uniform radial stress since this has been dealt with in several earlier publications.