Reaching ability of the paretic upper extremity in individuals with stroke decreases with increased shoulder abduction (SABD) loads. Transcranial direct current stimulation (tDCS) has been implemented to improve movement ability following stroke. However, results from previous studies vary, perhaps due to the influence of impairment level and the type of motor tasks that were used to study the effects of tDCS. This study specifically examines the impact of SABD loading on the effects of tDCS in 9 individuals with moderate to severe chronic stroke. In 3 different sessions, participants repeated a reaching assessment with various SABD loads (supported on a haptic table, 25%, and 50% of maximum voluntary SABD torque) in random order, pre and post one of the following 15-min tDCS protocols: anodal stimulation of lesioned M1, cathodal stimulation of non-lesioned M1, or anodal stimulation of non-lesioned M1. Sham stimulation was also conducted preceding one of the tDCS sessions. The averaged maximum reaching distance over valid trials was calculated for each condition. We observed significant interactions between SABD load, tDCS protocol and time (i.e., pre or post-tDCS). Post hoc test showed that anodal stimulation of the lesioned M1 caused a clear trend (p = 0.058) of increasing the reaching ability at a medium level of SABD loading (25%), but not for higher loads (50%). This suggests that anodal stimulation increases residual corticospinal tract activity, which successfully increases reaching ability at moderate loads; however, is insufficient to make significant changes at higher SABD loads. We also found that cathodal stimulation of the non-lesioned M1 significantly (p = 0.018) decreased the reaching distance at a high level of SABD loading (50%). This study demonstrated, for the first time, that the effect of tDCS on the reaching ability is dependent on SABD loads in individuals with moderate to severe stroke.