A test-day (TD) random regression model (RRM) was described for the genetic evaluation of somatic cell score (SCS) where first and later lactations were considered as two different but correlated traits. A two-step covariance function procedure was used to estimate variance-covariances and associated genetic parameters. Analysis of estimated breeding values (EBV), ranking of top bulls and cows and some computational aspects were used to compare RRM with TD repeatability model (RPM) and lactation average model (LAM). Residuals were analysed to assess the relative fit of TD models. Comparison between RRM and RPM showed that RRM has lower mean squared error and gave better fit to the data. For young bulls and cows, the standard deviation (SD) of EBVs was highest for RRM and lowest for LAM implying efficient utilization of information on SCS, in terms of revealing more genetic variation. A much lower correlation of EBVs ranging from 0.80 to 0.92 and significant re-ranking of top bulls and cows were observed between RRM and LAM. The lower across-lactation correlation between RRM and LAM indicated that LAM is directed to give more weight to first lactation breeding values. The RRM, where SCS in the first and later lactations was considered as two different but correlated traits was able to make effective use of available information on young bulls and cows, and could offer an opportunity to breeders to utilize EBVs for first and later lactations.