Transition amplitudes and transition probabilities for the two-photon 1s–2s transition in the hydrogen atom and 1¹s–2¹s transition in helium atom have been calculated using a partial-closure approach. The dominant term is calculated exactly and the remaining sum over intermediate states is calculated using a mean excitation energy. Our value of the transition amplitudes agree within 2% with the exact results for the hydrogen case. Our value of the transition probability for hydrogen is 8.50 s⁻¹ which is in good accord with its known value 8.226 s⁻¹. For helium, the photon energy distribution of the metastable 2¹s state is in good agreement with the accurate values. The corresponding transition probability is 53.7 s⁻¹ which is in good agreement with the accurate value 51.3 s⁻¹.