Quadrilateral or McPherson suspension with cross leaf spring, comprising - a lower oscillating arm having a first part hinged to a fixed part of a vehicle and a second part connected to a wheel hub, - a shock absorber having a first end hinged to said fixed part of the vehicle and a second end, opposite to the first one, hinged to said wheel hub or to said lower oscillating arm, - a leaf spring, defining a longitudinal development, arranged parallel to a symmetrical vehicle axle defined by the suspension, having an intermediate point of reference, an end point (L/2) connected to said lower arm and a constraint point (B2, 1/2), intermediate between the first two, constrained to said fixed part, wherein the following distances measured along said longitudinal development starting from said intermediate point of reference are defined: - P = distance of said connection between lower arm and wheel hub, - L/2 = distance from said end point (L/2) of the leaf spring, - H = distance of said hinging between said first part of the lower arm and said fixed part, - 1/2 = distance of said intermediate constraint point; wherein I/2 is smaller than H and the leaf spring comprises a portion having a constant thickness between said intermediate reference point and I/2 and a parabolic decreasing thickness between I/2 and L/2; characterized in that: - d is a difference/distance between H and L/2 and b a difference/distance between H and P, R = b / b − d, ks = ksosp * R 2, where 'ks' is the stiffness of the leaf spring upon symmetrical vertical loads and 'ksosp' is the stiffness of the suspension upon symmetrical vertical loads, wherein said parabolic thickness between I/2 and L/2 is defined by: h Y = 2 * Y − cost 1 / cost 2 0.5, where Y is an independent variable, cost 1 = 1015.00942 and cost 2 = -8.51224 and wherein the material of said leaf spring has a Young module comprised between 195 GPa and 210 GPa. - a lower oscillating arm having a first part hinged to a fixed part of a vehicle and a second part connected to a wheel hub, - a shock absorber having a first end hinged to said fixed part of the vehicle and a second end, opposite to the first one, hinged to said wheel hub or to said lower oscillating arm, - a leaf spring, defining a longitudinal development, arranged parallel to a symmetrical vehicle axle defined by the suspension, having an intermediate point of reference, an end point (L/2) connected to said lower arm and a constraint point (B2, 1/2), intermediate between the first two, constrained to said fixed part, - P = distance of said connection between lower arm and wheel hub, - L/2 = distance from said end point (L/2) of the leaf spring, - H = distance of said hinging between said first part of the lower arm and said fixed part, - 1/2 = distance of said intermediate constraint point; - d is a difference/distance between H and L/2 and b a difference/distance between H and P, R = b / b − d, ks = ksosp * R 2, where 'ks' is the stiffness of the leaf spring upon symmetrical vertical loads and 'ksosp' is the stiffness of the suspension upon symmetrical vertical loads, wherein said parabolic thickness between I/2 and L/2 is defined by: h Y = 2 * Y − cost 1 / cost 2 0.5, where Y is an independent variable, cost 1 = 1015.00942 and cost 2 = -8.51224 and wherein the material of said leaf spring has a Young module comprised between 195 GPa and 210 GPa.