The players were called off the show courts during their warm-up at Wimbledon on Thursday because of a light drizzle.
The women's singles semi-final between Serena Williams and Justine Henin-Hardenne and men's quarter-finals, Andy Roddick vs Jonas Bjorkman and Roger Federer vs Sjeng Schalken, were set to get underway on schedule at 1pm (1200 GMT) when the rain came.
The weather forecast predicts cloud and rain in the morning, followed by heavier showers in the afternoon, with the early evening bringing dark skies and possible problems with fading light.
The first week of the championships was relatively unaffected by the weather, but there have been interruptions every day in the second week.
Less than 2 1/2 hours' play was possible on the showcourts on Wednesday because of frequent rain and one spectacular storm.