A machine for making three-dimensional objects from powdered materials, comprising: a main body having a growing cavity extending along a main direction of extension; a growing platform for growing the object to be produced, slidably inserted in the growing cavity of the main body and movable along said main direction of extension between a plurality of operating positions; movement means for moving the growing platform; depositing means operatively associated with the growing cavity for depositing a succession of layers of powdered materials on the growing platform; an electromagnetic radiation device designed for focusing a beam of electromagnetic radiation on predetermined zones of each layer of deposited powder until joining together of the granules of powdered materials is achieved; an annular base body which can be operatively associated with the growing cavity of the main body for forming a narrowing of said growing cavity; said growing platform being interchangeable for adapting to said narrowing of the growing cavity; said machine being configurable between a first operating condition in which the annular base body is inserted in the growing cavity and a second operating condition in which the annular base body is removed from the growing cavity; characterised in that the growing cavity of the main body forms a channel passing through the main body and extending along the main direction of extension between an inlet end of the powdered materials and a mounting end for mounting the annular base body opposite to the inlet end; said annular base body being insertable in the growing cavity through the mounting end during the passage from the second operating condition to the first operating condition; said machine comprising fastening means interposed between the annular base body and the mounting end of the main body for fixing the annular base body to the main body. a main body having a growing cavity extending along a main direction of extension; a growing platform for growing the object to be produced, slidably inserted in the growing cavity of the main body and movable along said main direction of extension between a plurality of operating positions; movement means for moving the growing platform; depositing means operatively associated with the growing cavity for depositing a succession of layers of powdered materials on the growing platform; an electromagnetic radiation device designed for focusing a beam of electromagnetic radiation on predetermined zones of each layer of deposited powder until joining together of the granules of powdered materials is achieved; an annular base body which can be operatively associated with the growing cavity of the main body for forming a narrowing of said growing cavity; said growing platform being interchangeable for adapting to said narrowing of the growing cavity; said machine being configurable between a first operating condition in which the annular base body is inserted in the growing cavity and a second operating condition in which the annular base body is removed from the growing cavity; characterised in that the growing cavity of the main body forms a channel passing through the main body and extending along the main direction of extension between an inlet end of the powdered materials and a mounting end for mounting the annular base body opposite to the inlet end; said annular base body being insertable in the growing cavity through the mounting end during the passage from the second operating condition to the first operating condition; said machine comprising fastening means interposed between the annular base body and the mounting end of the main body for fixing the annular base body to the main body.