We investigated whether people take into account an interaction partner's attentional focus and whether they represent in advance their partner's part of the task when planning to engage in a synchronous joint action. The experiment involved two participants planning and performing joint actions (i.e., synchronously lifting and clinking glasses), unimanual individual actions (i.e., lifting and moving a glass as if clinking with another person), and bimanual individual actions. EEG was recorded from one of the participants. We employed a choice reaction paradigm where a visual cue indicated the type of action to be planned, followed 1.5 sec later by a visual go stimulus, prompting the participants to act. We studied attention allocation processes by examining two lateralized EEG components, namely the anterior directing attention negativity and the late directing attention positivity. Action planning processes were examined using the late contingent negative variation and the movement-related potential. The results show that early stages of joint action planning involve dividing attention between locations in space relevant for one's own part of the joint action and locations relevant for one's partner's part of the joint action. At later stages of joint action planning, participants represented in advance their partner's upcoming action in addition to their own action, although not at an effector-specific level. Our study provides electrophysiological evidence supporting the operation of attention sharing processes and predictive self/other action representation during the planning phase of a synchronous joint task.