•Bubble–bubble interaction can suppress or enlarge the radial pulsations of bubbles.•The suppression or enlargement depends on the ultrasound parameters, the radii, the distances and the bubble number.•The frequency response curve of expansion ratio decreases and shifts to left due to bubble–bubble interaction.•The larger the coupling strength is, the more the left-shifting is. Using a model that with or without considering the interaction between bubbles through the radiated pressure waves, numerical simulations of cavitation bubbles have been performed in order to study the effect of the bubble–bubble interaction on radial pulsations of bubbles. Comparing the results obtained by with or without considering the bubble–bubble interaction, it is suggested that the suppression or enlargement property of expansion ratios of bubbles due to the bubble–bubble interaction largely depends on the ultrasound parameters, the ambient bubble radii, the distances between bubbles and the number of bubbles (in multi-bubble environment, the last two aspects can be expressed using the coupling strength). The frequency response curve of expansion ratio decreases and shifts to left due to the bubble–bubble interaction and the larger the coupling strength is, the more the left-shifting is.