The cohesin complex is mutated in cancer and in a number of rare syndromes collectively known as Cohesinopathies. In the latter case, cohesin deficiencies have been linked to transcriptional alterations affecting Myc and its target genes. Here, we set out to understand to what extent the role of cohesins in controlling cell cycle is dependent on Myc expression and activity. Inactivation of the cohesin complex by silencing the RAD21 subunit led to cell cycle arrest due to both transcriptional impairment of Myc target genes and alterations of replication forks, which were fewer and preferentially unidirectional. Ectopic activation of Myc in RAD21 depleted cells rescued Myc-dependent transcription and promoted S-phase entry but failed to sustain S-phase progression due to a strong replicative stress response, which was associated to a robust DNA damage response, DNA damage checkpoint activation and synthetic lethality. Thus, the cohesin complex is dispensable for Myc-dependent transcription but essential to prevent Myc-induced replicative stress. This suggests the presence of a feed-forward regulatory loop where cohesins by regulating Myc level control S-phase entry and prevent replicative stress.