Single and multi-traits animal models were utilized to estimate variance and covariance components and genetic parameters of Wood's lactation curve parameters and associated traits in Zaraibi goats. A dataset comprising 1323 test day record collected from the Zaraibi herd at the El-Serw Experimental Station Damietta, Egypt between 2005 and 2014 were analyzed. Overall means of initial milk yield (a), ascending slope up to peak (b), descending slope after peak (c), persistency (S), weeks to peak (PW), and peak milk yield (PMY) were 1.504 kg, 0.421 kg, 0.098 kg, 1.433 kg, 4.295 weeks, and 1.823 kg, respectively. Heritability estimates for a, b, c, S, PW, and PMY were found to be 0.05 (0.06), 0.07 (0.07), 0.12 (0.14), 0.13 (0.13), 0.12 (0.14), and 0.11 (0.13), respectively, as indicated by single-trait (multi-trait) animal models, respectively. Strong positive genetic correlations were identified between various lactation curve traits varied between 0.72 and 0.91. Negative genetic correlation was observed between initial yield and both of ascending slope up to peak (-0.59) and time to peak (-0.38). Moreover, the ascending slope displayed a negative correlation with persistency (-0.32), while time to peak showed a positive correlation with ascending slope (0.37) and a negative correlation with descending slope (-0.58). In conclusion, the findings indicate slight discrepancies between single and multi-trait animal models in estimating variance components and genetic parameters. The moderate to high genetic correlations among lactation curve parameters and their related traits suggest that utilizing any of these parameters could effectively improve the traits' curves.