Quadrilateral or McPherson suspension (S) with cross leaf spring, comprising - a lower oscillating arm (AL) having a first part hinged to a fixed part (C) of a vehicle and a second part connected to a wheel hub (SP), - a shock absorber (SG) having a first end hinged to said fixed part (C) of the vehicle and a second end, opposite to the first one, hinged to said wheel hub (SP) or to said lower oscillating arm (AL), - a leaf spring (LS), defining a longitudinal development (Y), arranged parallel to a symmetrical vehicle axle defined by the suspension (S), having an intermediate point of reference (M), an end point (L/2) connected to said lower arm (AL) and a constraint point (B2, 1/2), intermediate between the first two, constrained to said fixed part (C), wherein the following distances measured along said longitudinal development (Y) starting from said intermediate point of reference (M) are defined: - P = distance of said connection (X2) between lower arm (AL) and wheel hub (SP), - L/2 = distance from said end point (L/2) of the leaf spring (LS), - H = distance of said hinging (X1) between said first part of the lower arm and said fixed part (C), - 1/2 = distance of said intermediate constraint point (B2); wherein I/2 is smaller than H and the leaf spring (LS) comprises a portion (h0) having a constant thickness between said intermediate reference point (M) 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 (AL) having a first part hinged to a fixed part (C) of a vehicle and a second part connected to a wheel hub (SP), - a shock absorber (SG) having a first end hinged to said fixed part (C) of the vehicle and a second end, opposite to the first one, hinged to said wheel hub (SP) or to said lower oscillating arm (AL), - a leaf spring (LS), defining a longitudinal development (Y), arranged parallel to a symmetrical vehicle axle defined by the suspension (S), having an intermediate point of reference (M), an end point (L/2) connected to said lower arm (AL) and a constraint point (B2, 1/2), intermediate between the first two, constrained to said fixed part (C), - P = distance of said connection (X2) between lower arm (AL) and wheel hub (SP), - L/2 = distance from said end point (L/2) of the leaf spring (LS), - H = distance of said hinging (X1) between said first part of the lower arm and said fixed part (C), - 1/2 = distance of said intermediate constraint point (B2); - 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. <EOS>