A numerical model of the behaviour of the magnetization in a field-cycled dynamic nuclear polarization (DNP) experiment is presented, with the aim of optimizing pulse sequence parameters in field-cycled proton–electron double-resonance free radical imaging. The model is used to predict the observed enhancement of the NMR signal as a function of the magnetic field strength, EPR irradiation frequency and pulse sequence timing, as well as the properties of the sample including the NMR and EPR relaxation times. The model allowed optimization of parameters in the field-cycled DNP experiment, in particular the EPR irradiation frequency, to find the value which would give the largest difference between NMR signals recorded with and without EPR irradiation. Experiments to verify the model were carried out using aqueous solutions of TEMPOL, which exhibits three hyperfine lines in its EPR spectrum and triarylmethyl (TAM), which has a single, narrow line. It was found that the model predicted very well the variation in DNP enhancement with EPR irradiation power for both samples. The behaviour of the NMR signal with EPR irradiation frequency in studies using TEMPOL was also accurately modelled, with the optimum frequency lying between 60 and 80 MHz, depending on the EPR irradiation power. The optimum frequency obtained from the model also agreed with the experimental data obtained using the TAM free radical, but with this sample the theoretical curves tended to deviate from the experimental data at irradiation frequencies below 70 MHz.