Ultrasound growth measurements are monitored to evaluate if a fetus is growing normally compared with a defined standard chart at a specified gestational age. Using data from the Fetal Growth Longitudinal Study of the INTERGROWTH-21st project, we have modelled the longitudinal dependence of fetal head circumference, biparietal diameter, occipito-frontal diameter, abdominal circumference, and femur length using a two-stage approach. The first stage involved finding a suitable transformation of the raw fetal measurements (as the marginal distributions of ultrasound measurements were non-normal) to standardized deviations (Z-scores). In the second stage, a correlation model for a Gaussian process is fitted, yielding a correlation for any pair of observations made between 14 and 40 weeks. The correlation structure of the fetal Z-score can be used to assess whether the growth, for example, between successive measurements is satisfactory. The paper is accompanied by a Shiny application, see https://lxiao5.shinyapps.io/shinycalculator/.