A total of 2590 records (1592 live and 998 dead rabbits) of livability (LIV), weaning weight (WWT) and average daily gain from birth till weaning weight (ADG) of rabbits as growth trait were obtained from 142 (96 dams and 46 does) exotic New-Zealand White (NZW) having 344 litters and 18 sires, raised at the experimental farm belonging to animal production research institute (APR!). Records were analyzed to obtain variance and (co) variance components of livability trait using Gibbs Sampling, WWT and ADG using MTDFREML procedures. The livability single trait analyzed using threshold animal model, while, 1NWT and ADG multi-traits were analyzed using animal model with the flat distribution. The Models included litter size at birth (lsb), weight of doe at conception , month of birth, year of birth and parity as fixed effects for (LIV) trait add to sex effect for WWT and ADG .The random effects in the models were additive genetic, maternal and permanent environmental effects. Gibbs Sampling (GS) heritability estimate for binary trait (LIV) was 0.44. The variances due to maternal and permanent environmental effects were 0.48 and 0.001 as a proportion of phenotypic variance, respectively. The correlation between direct genetic and maternal effect was -0.25. MTDFREML heritabilities estimates for (VVWT) and (ADG) were 0.55 and 0.75, respectively. The variance due to maternal and permanent environmental effects as a proportion of phenotypic variance for MT and ADG were 0.41, 0.30, .52 and .03, respectively. The correlation between WWT and ADG was 0.99.