Composites based on hardened alumina cement pastes reinforced with 3 to 10 wt.% of glass fibres were prepared for the purpose of increasing the bending strength of the refractory concrete at 500_C - 1000_C. On the basis of measuring Young's modulus and Poisson' constant of the model reinforced material (water-to-cement ratio 0.30, 5 wt.% of fibres) at 20_C; a simple isothermic mechanical model was proposed on the basis of Hook's law for a linear elastic continuum. The model describes the development of stress in the loaded material in the course of uniform compression up to the elasticity limit.