Our objective was to predict the dry matter intake (DMI) response during ration formulation to factors related to the filling effect of rations and their interaction with milk yield (MY) by lactating cows past peak lactation. A data set was developed consisting of 134 treatment means from 34 experiments reported in 32 peer-reviewed articles published from 1990 through 2015. The data set included data for cows ranging from 60 to 309 d postpartum with mean DMI ranging from 17.6 to 30.6 kg/d and MY ranging from 20.3 to 51.1 kg/d. Ration composition among treatments ranged from 12.7 to 21.8% of dry matter (DM) for crude protein, 11.5 to 31.0% of DM for acid detergent fiber (ADF), 25.5 to 48.2% of DM for neutral detergent fiber (NDF), 9.9 to 39.3% of DM for forage NDF (FNDF), and 0.45 to 0.84 for the ratio of ADF% to NDF% (ADF/NDF). Laboratory measures of digestibility of NDF (in vitro or in situ, FNDFD) for the sole or major forage ranged from 24.1 to 72.7%. The model included the random effect of study to account for various experiment-specific effects including different methods of measurement of NDF and FNDFD among studies. The full model also included linear and quadratic effects of crude protein, ADF, NDF, FNDF, ADF/NDF, and FNDFD, as well as their linear and quadratic interactions, and mean MY for each study and its interaction with ration factors. The proposed prediction equation is DMI (kg/d) = 12.0 - 0.107 × FNDF + 8.17 × ADF/NDF + 0.0253 × FNDFD - 0.328 × (ADF/NDF - 0.602) × (FNDFD - 48.3) + 0.225 × MY + 0.00390 × (FNDFD - 48.3) × (MY - 33.1) with mean bias = 0.00 kg/d, root mean square error = 1.55 kg/d, and concordance correlation coefficient = 0.827. Dry matter intake was positively related to MY and ADF/NDF and negatively related to FNDF, and FNDFD was positively related to DMI for cows with high MY but negatively related to MY for cows with low MY. In addition, DMI was positively related to FNDFD for low ADF/NDF but negatively related to FNDFD for high ADF/NDF. The ADF/NDF was included to represent differences in forage fragility between grasses and legumes. The proposed model was compared with the equation recommended by the National Research Council (2001) that was developed using only animal factors by fitting each equation to a subset of the data set that included the required inputs for both. The National Research Council (2001) equation without diet factors had a higher root mean square error and over-predicted DMI at high DMI and under-predicted DMI at low DMI. Our proposed equation should be useful to predict DMI response to factors related to the filling effects of rations during ration formulation.