The stress field developed in a circular semi-ring under the combined action of diametral compression and bending is explored both analytically and numerically. The analytic solution is implemented by means of the complex potentials technique as it was formulated by Muskhelishvili, while for the numerical study a finite element model, properly validated based on experimental data, is used. The analytic solution provided closed formulae for the stress field along strategic loci of the specimen, while the numerical model permitted thorough parametric investigation of the dependence of critical quantities on geometrical and loading factors. The idea behind the study is to assess the potentialities of the circular semi-ring as a possible substitute of the familiar Brazilian disc, in the direction of curing drawbacks of the latter. It was concluded that a circular semi-ring subjected to eccentric diametral compression provides reliable data for the tensile strength of very brittle materials, relieved from ambiguities characterizing the standardized Brazilian-disc test.