The Simon effect denotes superior performance when stimulus and response positions correspond than when they do not, even when stimulus position is irrelevant. Usually, this effect is attributed to the automatic formation of a spatial stimulus code that interferes with response selection. Recent evidence, however, called the hypothesis of automatic processing of stimulus position into question. The present study aimed at providing a strong test of this hypothesis. In two experiments, a dual-task procedure was employed. The primary task was an auditory-manual four-choice task (S1-R1 task). The secondary task was a visual encoding task (S2-R2 task), and S2 followed S1 with a variable stimulus onset asynchrony (SOA). Horizontal position of S2, which was irrelevant for both tasks, was also varied, and the effect of spatial S2-R1 correspondence was investigated. Experiment 1 showed dual-task impairment in visual encoding, and a cross-task Simon effect at short SOAs. That is, S2 position affected R1 selection, although less capacity was available for deliberately processing S2 position. In addition, Experiment 2 revealed the absence of the cross-task Simon effect when the target appeared simultaneously with a contralateral distractor. Together, the results suggest that encoding of stimulus position can run automatically, on the basis of an exogenous attention shift towards stimulus location.