Abstract: The group of inventions relates to the refractory materials industry, in particular to the production of refractory high-strength nonconductive articles of corundum and silicon carbide concretes on an aluminophosphate binder. The objective of the proposed group of inventions is to provide shaped thermoinsulative and thermoconductive concretes based on an aluminophosphate binder with high strength characteristics, enabling the concretes to be used as building and construction materials operating at high temperatures. According to the first variant, the thermoinsulative concrete based on an aluminophosphate binder includes a phosphate binder and a mixture, wherein orthophosphoric acid is used in a concentration of 65-75% as phosphate binder and a mixture of different fractions of 25A grade electrocorundum is used as the mixture.