This paper presents a novel method for detecting 3D road boundaries, such as walls, guardrails, and curbs, using on-board stereo cameras. The proposed method uses conformal geometric algebra, which can describe different shapes in a common representation. 3D road boundaries on straight and curved roads are seamlessly detected by use of this representation, and this framework is also applied to curb detection by a subtle modification. Experimental results show that despite its algorithmic simplicity, the proposed method exhibited competitive detection performance compared with conventional model fitting and curb detection methods.