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The paper presents a description of geometric models, computational algorithms, and results of numerical analysis of charge exchange in an opposed-piston two-stroke engine. The research engine is a newly designed internal diesel engine. This unit is composed of three cylinders in which operate three pairs of opposed-pistons. The engine generates a power output equal to 100 kW at a crankshaft rotation speed of 3800-4000 rpm. The numerical investigations were carried out using ANSYS FLUENT solver. The geometrical model includes an intake manifold, a cylinder and an outlet manifold. The study was conducted for a series of modifications of manifolds and intake and exhaust ports to optimise the charge exchange process in the engine. In addition, we attempted to verify the effect of the combustion chamber shape on the charge exchange process in the engine. The calculations specified a swirl coefficient obtained under steady conditions for fully open intake and exhaust ports as well as the CA value of 280° for all cylinders. In addition, mass flow rates were identified separately in all of the intake and exhaust ports to achieve the best possible uniformity of flow in particular cylinders. The paper includes comparative analyses of all of the intake and exhaust manifolds of the designed engine.