Stretchable organic light-emitting diodes (SOLEDs) based on buckled structures have been widely studied and offer broad application prospects in wearable electronics, deformable displays and electronic skin due to their high brightness and efficiency, large stretchability, and straightforward fabrication process. However, buckles are composed of a large number of wavy microstructures which bring large bending strain and uneven surface to the light-emitting regions. These negative factors increase the risk of device performance degradation, reduce the brightness uniformity, and distort the pixels. The negative effects are amplified by changes of the buckles' morphology during stretching. In this paper, we solve these issues in buckled SOLEDs by strain engineering. Strain isolation islands are introduced into the flexible substrate to bear the compressive stress from the elastic tape and protect the light-emitting regions from forming buckles. As a result, a buckled SOLED array with planar light-emitting regions have been obtained. It shows a maximum one-dimensional (1D) stretchability of 50 % and a two-dimensional stretchability (2D) of 30 %. The pixels in the SOELD array exhibit efficient, stable and uniform electroluminescent (EL) performance. After 1000 times of cyclic stretching, the current efficiency, shape and area of each pixel in the array barely change, demonstrating the potential of the SOLEDs for stretchable display applications.