Psychopathology is rooted in neurodevelopment. However, clinical and biological heterogeneity, together with a focus on case-control approaches, have made it difficult to link dimensions of psychopathology to abnormalities of neurodevelopment. Here, using the Philadelphia Neurodevelopmental Cohort, we built normative models of cortical volume and tested whether deviations from these models better predicted psychiatric symptoms compared to raw cortical volume. Specifically, drawing on the p-factor hypothesis, we distilled 117 clinical symptom measures into six orthogonal psychopathology dimensions: overall psychopathology, anxious-misery, externalizing disorders, fear, positive psychosis symptoms, and negative psychosis symptoms. We found that multivariate patterns of deviations yielded improved out-of-sample prediction of psychopathology dimensions compared to multivariate patterns of raw cortical volume. We also found that correlations between overall psychopathology and deviations in ventromedial prefrontal, inferior temporal, and dorsal anterior cingulate cortices were stronger than those observed for specific dimensions of psychopathology (e.g., anxious-misery). Notably, these same regions are consistently implicated in a range of putatively distinct disorders. Finally, we performed conventional case-control comparisons of deviations in a group of individuals with depression and a group with attention-deficit hyperactivity disorder (ADHD). We observed spatially overlapping effects between these groups that diminished when controlling for overall psychopathology. Together, our results suggest that modeling cortical brain features as deviations from normative neurodevelopment improves prediction of psychiatric symptoms in out-of-sample testing, and that p-factor models of psychopathology may assist in separating biomarkers that are disorder-general from those that are disorder-specific.