The co-occurrence of abuse of multiple substances is thought to stem from a common liability that is partly genetic in origin. Genetic risk may indirectly contribute to a common liability through genetically influenced individual vulnerabilities and traits. To disentangle the aetiology of common versus specific liabilities to substance abuse, polygenic scores can be used as genetic proxies indexing such risk and protective individual vulnerabilities or traits. In this study, we used genomic data from a UK birth cohort study (ALSPAC, N=4218) to generate 18 polygenic scores indexing mental health vulnerabilities, personality traits, cognition, physical traits, and substance abuse. Common and substance-specific factors were identified based on four classes of substance abuse (alcohol, cigarettes, cannabis, other illicit substances) assessed over time (age 17, 20, and 22). In multivariable regressions, we then tested the independent contribution of selected polygenic scores to the common and substance-specific factors. Our findings implicated several genetically influenced traits and vulnerabilities in the common liability to substance abuse, most notably risk taking (bstandardized=0.14; 95%CI: 0.10,0.17), followed by extraversion (bstandardized =-0.10; 95%CI: -0.13,-0.06), and schizophrenia risk (bstandardized=0.06; 95%CI: 0.02;0.09). Educational attainment (EA) and body mass index (BMI) had opposite effects on substance-specific liabilities such as cigarettes (bstandardized-EA= -0.15; 95%CI: -0.19,-0.12; bstandardized-BMI=0.05; 95%CI: 0.02,0.09), alcohol (bstandardized-EA=0.07; 95%CI: 0.03,0.11; bstandardized-BMI= -0.06; 95%CI: -0.10,-0.02), and other illicit substances (bstandardized-EA=0.12; 95%CI: 0.07,0.17;bstandardized-BMI= -0.08; 95%CI:-0.13,-0.04). This is the first study based on genomic data that clarifies the aetiological architecture underlying the common versus substance-specific liabilities, providing novel insights for the prevention and treatment of substance abuse.