The technique for growing low dislocation density GaAs crystal was studied with computer simulation and experiments. The studies consist of the following three subjects. (1) The thermal stress induced in the temperature range between 1100℃ and 1200℃ after solidification was investigated with simulation using finite element method. The low temperature gradient in the crystal after solidification and the direction of crystal growth were found to be effective for reducing dislocation density. (2) The dependence of EPD on crystal diameter and crystal cooling rate in the temperature range between 900℃ and 1200℃ was observed. (3) The correlation between the deviation of solid-liquid (S/L) interface from a flat plane and the dislocation density was found. By applying to 3T-HB method the results of the thermal stress analysis, the slow cooling rate and the control of S/L interface, Si doped GaAs with EPD≦400 cm^<-2> throughout the ingot has been grown.