In the past few years flat user interface design has become the predominating visual style of operating systems, websites and mobile apps. Although flat design has been widely criticized by HCI and usability experts, empirical research on flat design is still scarce. We present the results of an experimental comparative study of visual search effectiveness on traditional and flat designs. The following types of visual search tasks were examined: (1) search for a target word in text; (2) search for a target icon in a matrix of icons; (3) search for clickable objects on webpages. Time and accuracy parameters of the visual search, as well as oculomotor activity, were measured. The results show that a search in flat text mode (compared with the traditional mode) is associated with higher cognitive load. A search for flat icons takes twice as long as for realistic icons and is also characterized by higher cognitive load. Identifying clickable objects on flat web pages requires more time and is characterised by a significantly greater number of errors. Our results suggest replacing the flat style user interfaces with interfaces based on the design principles developed over decades of research and practice of HCI and usability engineering.