Ribbons and tubes grown from the melt by the Stepanov technique have a wide range of technical applications. Sapphire ribbons are used as substrates in microelectronics and sapphire tubes are used as gas-discharge balloons in laser engineering, fine chemical technology and high-vacuum equipment. Practice has shown that misorientation angles of small-angle boundaries in sapphire crystals should not exceed several degrees because an increase in the misorientation angles between blocks drastically lowers the strength and worsens the dielectric properties of these crystals. One of the main mechanisms of formation of the block structure of melt-grown crystals, including shaped sapphire crystals, is dislocation polygonization that begins when the dislocation density exceeds a certain critical value. In turn, dislocations are formed under deformations due to thermal stresses. Calculations of thermal fields in crystals and the corresponding thermoelastic stress fields can be used as an input to improve and optimize the growth process. The dependence of thermoelastic stresses in ribbons and tubes on the technological parameters has been calculated.