In a method of compressing stress data in a display device, the stress data is divided into block stress data for a pixel block, a plurality of compressed codes are generated by encoding the block stress data in a plurality of encoding modes, it is determined whether the plurality of encoding modes are available encoding modes for the block stress data based on code lengths of the plurality of compressed codes and a number of available bits for the pixel block, a final encoding mode is selected among the available encoding modes based on quantization values of the available encoding modes, and a compressed bitstream for the pixel block is generated based on a compressed code corresponding to the final encoding mode among the plurality of compressed codes.