The planar shape and size of joints have a profound effect on connectivity, permeability and stability of rock masses [1,2]. The planar shape and size of joints serve as the fundamental parameters to model three dimensional discrete joint networks which have been wildly used in various fields, such as nuclear waste disposal engineering [3], the mining industry [4] and hydraulic engineering [5]. Therefore, how to accurately determine the joint shape and its size distribution has been studied over decades. However, it is rarely known in practice that the real joint shape and size distribution, if measured directly, need to completely dismantle a given rock mass. There are two approaches in literature to deal with this problem. The first is the trial-and-error method and the second is the inference of the fracture size distribution from trace lengths on an infinite surface. In the first approach, the form and parameters of fracture size distribution are repeatedly adjusted until the error between the simulated trace length distribution and the observed one satisfies the requirement. This technique, known as “Forward modeling”, and the algorithm of searching best-fit distribution was proposed and developed by Dershowitz et al. [6,7] and Paul et al. [8]. Forward modeling is very useful for severely truncated data and is employed to various types of engineering, especially the hydraulic area [3,9,10]. In the second approach, the probability distribution function (PDF) of joint size is obtained from the true PDF of the trace length (i.e. trace length distribution in an infinite plane). PDF can be determined from natural outcrops, excavated faces sampling and correcting on the basis of stereological relationship and assumed joint shape. Warburton [11,12] made the hypothesis that joints are parallel to each other and in the planar shape of disks or parallelograms. Warburton also worked out the stereological relation between the PDF of trace length and PDF of joint size. Zhang et al. [13] followed Warburton's approach and obtained the similar relationships assuming that joints are elliptical. Decker and Mauldon [14] thought that joints in bedrock should be rectangular as they are terminated by primary joints. As for the procedure of obtaining joint size distribution, the main idea in literature is to assume a theoretical distribution and computing its moments at first, then apply Crofton's theorem which relates the moments of trace length with joint size to calculate the parameters of this assumed distribution [15–17]. Song [18,19] developed and applied a numerical technique to obtain the fracture diameter distribution from the trace length distribution. Tonon and Chen [20] calculated the PDF of circular joint diameters directly using Santalo transformation. The results obtained by the scholars above have a significant effect on engineering. However, due to the complexity of natural elliptical joints and singularities aroused in the stereological formula, the analytic solution for elliptical joint size distribution remains largely unknown. In this paper, an attempt is made to obtain the stereological relationship between trace length and size distribution when the joints are assumed to be non-parallel elliptical joints while many types of joint shape can be represented as ellipses [21]. An attempt to transform this stereological relationship into Abel type integral using an intermediate function and the inverse type of the integral is made as well. The PDF of joint size is derived by employing the