The noise levels generated by an unmuffled engine exhaust system can be identified as the loudest vehicle noise source. The muffler or silencer is an essential component of the internal combustion engine exhaust system. Its main function is to reduce the exhaust-generated noise to an acceptably low level. Its design development is a complex process affecting the engine efficiency and thus fuel consumption, emissions and overall noise generation. This paper focuses on the design development of a muffler for a single-cylinder engine application. A 1D GT-Power model of a single valve engine was developed. Additionally, an analytical muffler preliminary design methodology was introduced. The methodology provides guidelines for muffler grade selection, sizing of different components, and calculation of backpressure as a function of the exhaust gas flow rate. Two custom mufflers design concepts were developed for the single-cylinder engine based on the introduced analytical methodology. Two commercial single-cylinder engine muffler designs available from Yanmar and Loncin were considered for the engine performance evaluation simulation. The presented combination of analytical and numerical modelling procedures can reduce the overall length of the muffler development stage by eliminating faulty design concepts and refining the muffler's performance parameters.