Two personality dimensions, alexithymia and reward sensitivity, are known risk factors for problematic alcohol consumption. Internal or mood-change motives of drinking to cope with negative mood, as well as drinking to enhance positive mood (“get high”), have also been implicated as risk factors. The present study sought to determine whether the association between alexithymia and risky drinking is mediated by the motive of drinking to cope with negative mood, and whether the association between reward sensitivity and risky drinking is mediated by the motive of drinking to enhance positive mood. Social drinkers aged 18–45 years were recruited from an Australian university and the local community, with the final sample consisting of 155 participants (80 females, 75 males). They completed an online questionnaire battery that included the Toronto Alexithymia Scale (TAS-20), Depression Anxiety Stress Scales 21 (DASS-21), Drinking Motives Questionnaire – Revised (DMQ-R), Sensitivity to Punishment and Sensitivity to Reward Questionnaire (SPSRQ), and Alcohol Use Disorders Identification Test (AUDIT). The positive relationship between TAS-20 alexithymia and AUDIT index of risky drinking was mediated by coping motives for drinking, with the relationship of TAS-20 to the latter mediated by negative mood as indexed by DASS-21. Further, the positive relationship between SPSRQ sensitivity to reward scores and AUDIT was mediated by enhancement motives for drinking. Although results were obtained in a non-clinical sample, they are consistent with the differential drinking motives said to characterize Type I versus Type II alcoholism and suggest distinct trajectories from inherent personality traits to problematic drinking.