Background. Unfortunately, the COVID-19 pandemic is still far from stabilizing. Of particular concern is the sharp increase in the number of diseases in June-July, September-October 2020 and February-March 2021. The causes and consequences of this sharp increase in the number of cases are still waiting for their researchers, but there is already an urgent need to assess the possible duration of the pandemic, the expected number of patients and deaths. Correct simulation of the infectious disease dynamics needs complicated mathematical models and many efforts for unknown parameters identification. Constant changes in the pandemic conditions (in particular, the peculiarities of quarantine and its violation, situations with testing and isolation of patients) cause various epidemic waves, lead to changes in the parameter values of the mathematical models. Objective. In this article, pandemic waves in Ukraine will be detected, calculated and discussed. The estimations for durations and final sizes of the epidemic waves will be presented. Methods. We propose a simple method for the epidemic waves detection based on the differentiation of the smoothed number of cases. We use the generalized SIR (susceptible-infected-removed) model for the dynamics of the epidemic waves. The known exact solution of the SIR differential equations and statistical approach were used. We will use different data sets for accumulated number of cases in order to compare the results of simulations and predictions. Results. Nine pandemic waves were detected in Ukraine and corresponding optimal values of the SIR model parameters were identified. The number of cases and the number of patients spreading the infection versus time were calculated. In particular, the pandemic in Ukraine probably began in January 2020. If current trends continue, the end of the pandemic should be expected no earlier than in summer 2021. Conclusions. The differentiation of the smoothed number of cases, the SIR model and statistical approach to the parameter identification are helpful to select COVID-19 pandemic waves and make some reliable estimations and predictions. The obtained information will be useful to regulate the quarantine activities, to predict the medical and economic consequences of the pandemic.