The presence of h-BN phase in the composites, in which it is fulfilling a role of a solid lubricant, causes the appearance of the anisotropy of the elastic properties and thermal properties. In order to assess the extent of the phenomenon, velocity changes of ultrasonic wave propagation were measured and thermal conductivity changes were researched. Measurements were carried out on composites of alumina matrix, which had h-BN introduced in an amount of 0-30 vol.%. The study included measurements of the speed of propagation of ultrasound waves and thermal conductivity, which were made in two directions, namely, perpendicular and parallel directions to the axis of compression. Strong dependence of the thermal conductivity anisotropy of the phase composition of materials was revealed.