The present study aimed to evaluate the genetic parameters of first parity reproductive traits. Information on 762 reproductive records on Saanen × Beetal (S × B) goats reared for approximately five decades was collected from ICAR‐National Dairy Research Institute, Karnal, Haryana (1973–2020). For genetic analysis, single‐trait and multiple‐trait animal models were used. Gibbs sampler for animal model (GSAM) approach was used for estimating (co)variance components of reproductive traits. Six different single‐trait animal models (with or without maternal and environmental effects) were used and the deviance information criterion (DIC) determined the best model. The least squares mean for age at first service (AFS), age at first kidding (AFK), service period (SP), dry period (DP), gestation length (GL), kidding interval (KI), litter weight (LW), number of kids born (NKB) and number of female kids born (NFKB) in first parity were 526.99 ± 4.86, 662.96 ± 5.03, 219.11 ± 6.25, 109.38 ± 6.00, 150.48 ± 0.27, 356.63 ± 4.80 days, 3.87 ± 0.05 kg, 1.27 ± 0.02 and 0.67 ± 0.03, respectively. Lower heritability estimates for these reproductive traits revealed a sparse scope for genetic improvement. Multivariate analysis using Model 1 was carried out to evaluate the genetic and phenotypic correlation of these nine reproductive traits. The genetic correlation of DP and SP was negatively with LW, NKB and NFKB, which is favourable as reduction in SP and DP can improve these economically important traits through indirect selection. Consistent efforts towards genetic improvement of these goat flock poses a promising future for meat industry owing to high prolificacy and good reproductive potential in this flock.