Multivariate meta-analysis allows the joint synthesis of multiple correlated outcomes from randomised trials, and is an alternative to a separate univariate meta-analysis of each outcome independently. Usually not all trials report all outcomes; furthermore, outcome reporting bias (ORB) within trials, where an outcome is measured and analysed but not reported on the basis of the results, may cause a biased set of the evidence to be available for some outcomes, potentially affecting the significance and direction of meta-analysis results. The multivariate approach, however, allows one to ‘borrow strength’ across correlated outcomes, to potentially reduce the impact of ORB. Assuming ORB missing data mechanisms, we aim to investigate the magnitude of bias in the pooled treatment effect estimates for multiple outcomes using univariate meta-analysis, and to determine whether the ‘borrowing of strength’ from multivariate meta-analysis can reduce the impact of ORB. A simulation study was conducted for a bivariate fixed effect meta-analysis of two correlated outcomes. The approach is illustrated by application to a Cochrane systematic review. Results show that the ‘borrowing of strength’ from a multivariate meta-analysis can reduce the impact of ORB on the pooled treatment effect estimates. We also examine the use of the Pearson correlation as a novel approach for dealing with missing within-study correlations, and provide an extension to bivariate random-effects models that reduce ORB in the presence of heterogeneity. Copyright © 2012 John Wiley & Sons, Ltd.