A quench boiler is the key equipment in ethylene production for the rapid cooling of high-temperature cracking gas. In the boiler, heat transfer is occurs between the hot cracking gas passing through the inner heat exchange tubes with an average temperature of 385 °C and cold water (or boiler water) passing through the inner heat exchange tubes with an average temperature of 350 °C. Required for double-pipe heat transfer, special tubesheets formed by welding flat-round tubes side by side are difficult to design, as no suitable design code is available. The thermal expansion difference between the inner heat exchange tubes and the jacketed tubes could lead to high thermal stress on the tubesheet. In this study, we investigated the effects of pretension or prestretching of the heat exchange tubes on stress distribution and strength assessment of the flat-round tubesheet in a quench boiler under two dangerous load conditions. Results show that without prestretching the heat exchange tubes, the flat-round tubesheet cannot pass the strength assessment. Prestretching the heat exchange tubes is necessary, and a pretension of 9 mm is most suitable. The magnitude of the pretension of the heat exchange tubes should be determined based on the thermal expansion difference between the inner heat exchange tubes and the jacketed tubes, with consideration of the strength improvement of the flat-round tubesheet.