The effect of the modulation amplitude M on the true linewidth ΔH and on the displacement δH of the position of the peak signal relative to the resonant magnetic field is considered for magnetic resonance in samples of metals with dimensions large compared with the skin depth in the region of the classical skin effect. R, the main parameter in the theory of the lineshape, is (T_D/T₂)^1/2, where T_D is the time taken by an average electron to diffuse through the skin depth and T₂ is the electron spin relaxation time. Results are valid for resonance of conduction electrons (typically R <or= 0·5), static paramagnetic ions frozen in a metal and nuclei (large values of R). Calculated results, expressed in graphical and tabular form, are in terms of parameters relevant to the experimentalist and enable ΔH, T₂ and the resonant magnetic field to be obtained from modulation broadened lineshapes.ΔH is broadened by 5% when M/ΔH_m = 0·22, 0·24, 0·27 for R = 0·1, 0·5, 10 respectively. (ΔH_m is the measured linewidth.) The shift of the peak δH is always less than 1% of ΔH when R = 0·1; δH/ΔH = 0·01, 0·03 when M/ΔH_m, R, have values 0·24, 0·5 and 0·27, 10 respectively.Experimental measurements of the broadening of the resonance for conduction electrons in samples of Na and Li are in agreement with the calculations.