Predictors of problematic smartphone use have been found mainly in studies on elementary and high school students. Few studies have focused on predictors related to social network and messaging apps or smartphone model. Thus, the objective of our study was to identify predictors of problematic smartphone use related to demographic characteristics, loneliness, social app use, and smartphone model among university students. This cross-sectional study involved 257 Brazilian university students who answered a smartphone addiction scale, a questionnaire about smartphone usage patterns, and the Brazilian version of the UCLA-R loneliness scale. Women, iPhone owners, and users of Instagram and Snapchat had significantly higher smartphone addiction scores. We found correlations between scores for the Brazilian version of smartphone addiction scale and the importance attributed to WhatsApp, Facebook, Instagram, and Snapchat, and the Brazilian version of the UCLA-R loneliness scale. Our hierarchical regression model predicted 32.2% of the scores of the Brazilian version of the smartphone addiction scale, with the greatest increase in predictive capability by the step that added smartphone social app importance, followed by the step that added loneliness. Adding the smartphone model produced the smallest increase in predictive capability. The theoretical and practical implications of these results are discussed.