This study aimed to estimate genetic parameters for cumulative survival traits from birth to yearling age and to estimate their genetic relationship with birth weight in Guilan sheep. The dataset used in this study comprised 41,037 survival records of Guilan lambs born from 496 sires and 10,256 dams, collected by the Guilan Province Agricultural Jihad Organization (in Rasht, Iran) during 1990-2013. The data included complete pedigree information; gender; year, month, and day of death; dam age; year, month, and day of birth; birth type; and birth weight. Cumulative survival traits from birth to yearling age were analyzed using threshold animal models via the Bayesian method. Also, linear-threshold animal models were used to study the genetic relationship between survival at different ages and birth weight. Direct heritability estimates of cumulative survival from birth to 60, 90, 180, 270, and 365days of age were low and equal to 0.17, 0.16, 0.08, 0.04, and 0.04, respectively, and the corresponding maternal heritability estimates were 0.21, 0.18, 0.15, 0.08 and 0.08, respectively. Mean estimates of direct genetic correlations between birth weight and survival traits were medium (from 0.22 to 0.28). To improve the survival traits, more emphasis must be put on the amelioration of the non-genetic factors affecting it. Indirect selection based on traits high genetically correlated with survival could increase the survival rate in Guilan lambs.