A computer-implemented method for designing gradient coils for an MRI system configured to generate a static magnetic field, the gradient coils being configured for providing a current distribution on a lateral surface of an elliptical cylinder to generate a gradient magnetic field being perpendicular to a longitudinal axis of the elliptical cylinder, the method comprising the following steps: a) defining an imaging volume as an ellipsoid; b) defining an elliptic-cylindrical surface enclosing said ellipsoid; c) defining a current density at each point of the elliptic-cylindrical surface by a series of basis functions and corresponding coefficients expressed in elliptic cylindrical coordinates; d) describing the magnetic field generated at a generic point by the above defined current density integrated all over the entire elliptic-cylindrical surface; e) determining values of the coefficients of the basis functions by solving an inverse function for describing the magnetic field, thereby defining a continuous current density on the elliptic-cylindrical surface; f) generating a discrete winding pattern of a gradient coil from the continuous current density by using a stream function method and by using a series of scattered contours of the stream function as the design of the winding pattern according to a set total number of windings, wherein the winding pattern extension on the elliptic-cylindrical surface is delimited to opposed spaced away sectors of Lhe said elliptic-cylindrical surface by leaving open passages between the winding pattern of the gradient coil, wherein the minor axis of the elliptic-cylindrical surface is parallel to the static magnetic field of the MRI system and wherein said open passages are located at opposite sides of the elliptic-cylindrical surface in such a manner that the major axis of the elliptic-cylindrical surface intersects each open passage. the gradient coils being configured for providing a current distribution on a lateral surface of an elliptical cylinder to generate a gradient magnetic field being perpendicular to a longitudinal axis of the elliptical cylinder, the method comprising the following steps: a) defining an imaging volume as an ellipsoid; b) defining an elliptic-cylindrical surface enclosing said ellipsoid; c) defining a current density at each point of the elliptic-cylindrical surface by a series of basis functions and corresponding coefficients expressed in elliptic cylindrical coordinates; d) describing the magnetic field generated at a generic point by the above defined current density integrated all over the entire elliptic-cylindrical surface; e) determining values of the coefficients of the basis functions by solving an inverse function for describing the magnetic field, thereby defining a continuous current density on the elliptic-cylindrical surface; f) generating a discrete winding pattern of a gradient coil from the continuous current density by using a stream function method and by using a series of scattered contours of the stream function as the design of the winding pattern according to a set total number of windings, wherein the winding pattern extension on the elliptic-cylindrical surface is delimited to opposed spaced away sectors of Lhe said elliptic-cylindrical surface by leaving open passages between the winding pattern of the gradient coil, wherein a) defining an imaging volume as an ellipsoid; b) defining an elliptic-cylindrical surface enclosing said ellipsoid; c) defining a current density at each point of the elliptic-cylindrical surface by a series of basis functions and corresponding coefficients expressed in elliptic cylindrical coordinates; d) describing the magnetic field generated at a generic point by the above defined current density integrated all over the entire elliptic-cylindrical surface; e) determining values of the coefficients of the basis functions by solving an inverse function for describing the magnetic field, thereby defining a continuous current density on the elliptic-cylindrical surface; f) generating a discrete winding pattern of a gradient coil from the continuous current density by using a stream function method and by using a series of scattered contours of the stream function as the design of the winding pattern according to a set total number of windings, wherein the winding pattern extension on the elliptic-cylindrical surface is delimited to opposed spaced away sectors of Lhe said elliptic-cylindrical surface by leaving open passages between the winding pattern of the gradient coil, wherein the minor axis of the elliptic-cylindrical surface is parallel to the static magnetic field of the MRI system and wherein said open passages are located at opposite sides of the elliptic-cylindrical surface in such a manner that the major axis of the elliptic-cylindrical surface intersects each open passage.