An attempt is made to use the simplest epidemic models: SIR and SEIR to predict the spread of COVID-19 in Russia. Simplicity and a small number of parameters are very significant advantages of SIR and SEIR models in conditions of a lack of numerical initial data and structural incompleteness of models. The forecast of distribution of COVID-19 in Russia is carried out according to public data sets from March 10 to April 20, 2020. Comparison of forecast results by SIR and SEIR models are given. In both cases, the peak number of infected persons while maintaining the current level of quarantine measures is forecasted at the end of May 2020.