Despite the high potential of the freeze-casting technique for production of porous inorganic substrates, there is a lack of studies on tubular geometries and their mechanical behavior under different pressure scenarios. In this work, the mechanical behavior of tubular freeze-cast alumina substrates was assessed by mathematical models from experimental O-ring tests. The stress distributions revealed a concentration of tensile stresses (within 0.2-25.0 MPa) on the plane of the load, causing brittle fracture. Furthermore, the results confirmed that the honeycomb model for brittle material adequately predicted the mechanical strength of the tubular freeze-cast substrates. Finally, fracture criteria from honeycomb model was used to estimate the maximum homogeneously distributed pressures, such as in fluids, that the substrates can withstand. This configuration represents more precisely practical conditions, though is hard to experimentaly replicate. Therefore, the developed procedure is paramount to simulate the mechanical behaviour of the tubular freeze-cast substrates under real operating conditions.