Predicting the isotopic modification of ice by melting processes is important for improving the accuracy in paleoclimate reconstruction. To this end, we present results from cold room laboratory observations of changes in the isotopic ratio (D/H and 18O/16O) of ice cubes by isotopic exchange between liquid water and ice in nearly isothermal conditions. A 1-D model was fit to the isotopic results by adjusting the values of two parameters, the isotopic exchange rate constant (kr) and the fraction of ice participating in the exchange (f). We found that the rate constant for hydrogen isotopic exchange between liquid water and ice may be greater (up to 40%) than that for the oxygen isotopic exchange. The range of the rate constant obtained from four melt experiments is from 0.21 to 0.82 h–1. The model results also suggest that f decreases with the increasing wetness of the ice. This is because with increasing water saturation in ice, water may be present only in the small pores or some of the water that was exchanged with ice may be bypassed, decreasing the effective surface area over which the isotopic exchange can occur. The relationship between the two water isotopes (δ18O vs δD) was observed and modeled and the slope was <8, which is significantly different from the slope of the meteoric waterline. We note that these slopes were obtained without considering the sublimation process.