The invention relates to a machine for orienting and aligning articles, of the type that comprises: orientation cavities which can move along a closed path and which are equipped with an upper inlet for loading articles and an open base through which the articles can pass, a plurality of aligning conduits which are disposed below the orientation cavities, means for temporarily supporting the articles in the orientation cavities and for dropping same into the conduits, and support and/or end stop elements in each of the orientation cavities. In addition, each of the cavities comprises several seats or housings at different positions for receiving a first support and/or end stop element of the aforementioned support and/or end stop elements and retaining means for retaining said first support and/or end stop element in any of the seats or housings.