In this paper, we present an experimental study of the normal stress differences that arise in non-Brownian rigid fiber suspensions subject to a shear flow. While early measurements of the normal stress in fiber suspensions in Newtonian fluids measured only N-1 - N-2, the recent work of Snook et al. [ J. Fluid Mech. 758, 486-507 ( 2014)] and the present paper provide the first measurements of N-1 and N-2 separately. Snook et al. [ J. Fluid Mech. 758, 486-507 ( 2014)] perform such measurements with a gap that is very wide compared with the fiber length, whereas the present paper explores the effects of confinement when the gap is 4-10 times the fiber length. The first and the second normal stress differences are measured using a single experiment which consists of determining the radial profile of the second normal stress, along the velocity gradient direction, Sigma(22), in a torsional flow between two parallel disks. Suspensions are made of monodisperse fibers immersed in a neutrally buoyant Newtonian fluid. Two fiber lengths and three aspect ratios a(r) = L/d, and a wide range of concentrations have been tested. N-1 is found to be positive while N-2 is negative and the magnitude of both normal stress differences increases when nL(2)d increases, n being the number fraction of fibers. The magnitude of N-2 is found to be much smaller than N-1 only for high aspect ratios and low fiber concentrations. Otherwise, N-1 and N-2 are of the same order of magnitude. This is in contradiction with what is often assumed ( i. e., vertical bar N-2 vertical bar << N-1) but consistent with the recent numerical work of Snook et al. [ J. Fluid Mech. 758, 486-507 ( 2014)] that includes contact interactions. The effect of confinement on N-1 and N-2 is studied and it is shown that the more confined the suspension, the greater the magnitude of the normal stress differences. At last, the surface properties of the fibers are changed and the impact on the normal stress differences is discussed. (C) 2016 The Society of Rheology.