A mineral material processing plant includes a frame having two or more upper support surfaces and a jaw crusher including a crusher body having at least two bottom support surfaces at a distance from each other. The processing plant further includes at least one damper to be arranged in between the bottom and upper support surfaces which damper includes a first counter surface for the bottom support surface and a second counter surface for the upper support surface and an elastic material layer between the counter surfaces and preferably a slide joint between the first counter surface and the bottom or upper support surface. A method for damping a jaw crusher in a mineral material processing plant is also disclosed.