Multiple sclerosis (MS) patients often complain about balance problems when Romberg's test and tandem gait are normal. The aim of the study was to determine if measures of trunk sway taken during a battery of stance and gait tasks could be used to detect subclinical balance disorders. We recorded trunk angular sway in the pitch and roll directions from 20 MS patients (EDSS 1.4 ± 0.5) and 20 age- and gender-matched healthy controls (HCs), during 12 stance and gait tasks. We filmed 22 subjects simultaneously. Two neurologists assessed the videos, deciding whether task performance was pathological. Sway measures were significantly different between patients and HCs in eight out of 12 balance tasks. The most significant differences between MS patients and HCs were pitch angle range standing on one leg with eyes open on a firm surface (mean 3.13° vs. 2.09°, p = 0.005), and on a foam support surface (mean 6.24° vs. 2.96°, p = 0.006), pitch velocity range walking 8 m with eyes closed (mean 75.5 vs. 50.2°/s, p < 0.001) and pitch velocity range walking 3 m on heels (mean 85.37 vs. 60.9°/s, p = 0.002). Multivariate analysis revealed a model with three tasks which detected balance disorders in 84% of the MS patients and 90% of the HCs correctly. The neurologists achieved accuracies of 30% for the MS patients and 82% for the HCs. Using trunk sway measures during stance and gait tasks is a sensitive screening method for balance problems in MS patients, and is more accurate than assessment by trained neurologists.