Responses of elastic rods and shear beams with random field properties and also possibly under random field forcing are studied for random fields with linear, Matern, Cauchy, and Dagum covariances. The latter two allow decoupling of the fractal dimension and Hurst effect. The authors find second order characteristics of the beam displacement under clamped-free boundary conditions. Overall, for a given variance, the variance of the output is strongest for linear, then Matern, then Cauchy, and, finally, Dagum forcing. This is interesting and counterituitive because the Dagum and Cauchy models grasp the fractal characteristics and, additionally, the Hurst effect. In a number of (simpler) cases the results may be obtained in explicit analytical forms, but as Cauchy and Dagum models are introduced, one has to resort to numerics. (C) 2015 American Society of Civil Engineers.