In an engine operated machine, an engine and a generator formed integrally with each other are covered with a shroud and a fan cover to form a power-generating unit. A head cover of the engine is mounted to protrude from an upper surface of the shroud, and the head cover is resiliently supported on a carrying handle of a case with a rubber bushing positioned therebetween. When the carrying handle is lifted, the weight of the power-generating unit is supported directly by the carrying handle without being applied to the case. Therefore, it is unnecessary to specially reinforce the case, thereby enabling a reduction in weight, and also increasing the degree of freedom of the design such as the shape and material of the case. Thus, when the engine operated machine is transported using the carrying handle, the weight of the engine and the working device can be reliably supported. And a head cover of the engine is fixed to the carrying handle of the case, the air baffle plate defining the air passage in cooperation with the shroud, is formed integrally on the head cover and hence, the flow of the cooling air within the shroud can be smoothened.