Abstract Two vertical and orthogonal systematic joint sets are generally arrayed in a grid pattern on the bedding surface, which are the significant features of flat-lying sandstone terrains. Although extensive researches are reported on this topic, many fundamental problems have still not been solved. Such mutually perpendicular opening-mode fractures are an obvious manifestation of effective tensile stresses in two orthogonal directions in the horizontal bedding plane. A good understanding of these orthogonal joint systems is a key to structural analysis, landscape interpretation, and guidance of resolving a number of very practical problems in engineering, mining and hydrologic projects. Based on an anatomic investigation on the orthogonal joints in the Potsdam sandstone of Cambrian age at Ausable Chasm (New York State, USA) and Beauharnois (Quebec, Canada), we proposed that the orthogonal joints may result from the auxetic effects of quartz-rich sandstone rather than local or regional rotation of the maximum tensile stress (σ3) direction by about 90°. The sandstone beds with negative Poisson's ratios are so fascinating that, when placed under vertical burial compression and layer-parallel extension in one direction (σ3), it becomes stretched in the transverse direction (σ2), producing two orthogonal sets of mutual abutting and intersecting joints (J1 and J2 normal to σ3 and σ2, respectively), and both are normal to the bedding surface. Joint set J1 is more closely-spaced than J2 by a factor of ∼3.3, which is correlated with an average Poisson's ratio of −0.3 for the Potsdam sandstone at the time of joint formation.