Machine for preparing substances for intravenous application which comprises: - an initial container reception zone, which defines a matrix of individual initial container reception zones, with the individual initial containers (61, 61', 61") arranged along two horizontal axes which are perpendicular to each other, - a final container reception zone, which defines a matrix of individual final container reception zones, with the individual final containers (71, 71', 71") arranged along two horizontal axes which are perpendicular to each other, - a substance transfer circuit which comprises a set of devices (31, 32, 33) for extracting a substance from each individual initial container (61, 61', 61"), flexible tubes (9, 9', 9") and devices (41, 42, 43) for introducing substance into a final container (71, 71', 71"), said extraction devices (31, 32, 33) being in a linear arrangement, so as to form a vector of extraction devices (31, 32, 33) parallel to one of said axes of the matrix of individual initial container reception zones, each extraction device (31, 32, 33) being connected to one of said flexible tubes, and each flexible tube (9, 9', 9") being connected to one of said devices for introducing a substance into a final container (71, 71', 71"), by means of a pump (51, 52, 53), the substance introduction devices also being in a linear arrangement to each other, so as to form a vector of introduction devices (41, 42, 43), and in which the initial container reception zone or the vector of extraction devices (31, 32, 33) or both are capable of relative movement along a horizontal axis perpendicular to the vector of extraction devices, and/or the final container reception zone and the vector of introduction devices (41, 42, 43) are capable of relative movement along a horizontal axis perpendicular to the vector of introduction devices, in that the introduction devices (41, 42, 43) and the extraction devices (31, 32, 33) have the ability to move vertically, so that they can connect to/disconnect from the respective containers (71, 71', 71"; 61, 61', 61"), wherein each of the introduction or extraction devices has the ability to move vertically independently of the rest of the devices in its vector. - an initial container reception zone, which defines a matrix of individual initial container reception zones, with the individual initial containers (61, 61', 61") arranged along two horizontal axes which are perpendicular to each other, - a final container reception zone, which defines a matrix of individual final container reception zones, with the individual final containers (71, 71', 71") arranged along two horizontal axes which are perpendicular to each other, - a substance transfer circuit which comprises a set of devices (31, 32, 33) for extracting a substance from each individual initial container (61, 61', 61"), flexible tubes (9, 9', 9") and devices (41, 42, 43) for introducing substance into a final container (71, 71', 71"), said extraction devices (31, 32, 33) being in a linear arrangement, so as to form a vector of extraction devices (31, 32, 33) parallel to one of said axes of the matrix of individual initial container reception zones, each extraction device (31, 32, 33) being connected to one of said flexible tubes, and each flexible tube (9, 9', 9") being connected to one of said devices for introducing a substance into a final container (71, 71', 71"), by means of a pump (51, 52, 53), the substance introduction devices also being in a linear arrangement to each other, so as to form a vector of introduction devices (41, 42, 43), and in which the initial container reception zone or the vector of extraction devices (31, 32, 33) or both are capable of relative movement along a horizontal axis perpendicular to the vector of extraction devices, and/or the final container reception zone and the vector of introduction devices (41, 42, 43) are capable of relative movement along a horizontal axis perpendicular to the vector of introduction devices, in that the introduction devices (41, 42, 43) and the extraction devices (31, 32, 33) have the ability to move vertically, so that they can connect to/disconnect from the respective containers (71, 71', 71"; 61, 61', 61"), wherein each of the introduction or extraction devices has the ability to move vertically independently of the rest of the devices in its vector.