McLaren's Sergio Perez says the drivers are worried about the number of tyre failures in Formula 1.
Force India's Paul di Resta suffered a tyre delamination in practice at the Spanish GP, after three similar failures at the last race in Bahrain.
Perez said: "It's a big concern for all of us. You see two or three cars every weekend having this problem. There can be a really serious accident."
Pirelli motorsport boss Paul Hembery said they were looking for a solution.
Hembery said on Saturday that investigations had proved the failure was caused by debris and that the reason tyres are tending to strip rather than deflate this season is that they have made the internal belt stronger.
"It's similar to the failures of the other tyres we've seen this season," Hembery said. "When we made the move to putting high-tensile steel in the belt pack, when you get debris cutting the tyre it doesn't penetrate it.
"Instead the tread heats up and comes away. Last year it would probably have deflated on the rim and gone down immediately. So we've changed the mode of failure. You could argue it's safer because the tyre hasn't gone down.
"We would have to look at changing some parts of the structure, which is something we can do," Hembery added.
"But we would need to balance that with what impact it might have on the teams because they have a lot of data that's based on this year's structure which influences aerodynamics.
"Also there is a lack of testing. Some of the solutions we might need would need some more extensive testing, so we are caught in between a bit of a rock and a hard place.
"But we do take these things seriously. We're looking at it to see if we can change this mode of failure, the visibility of it and turn it into something that is less dramatic from a visual point of view."
Speaking on Friday after the failure, he said Pirelli were researching ways of preventing such failures happening.
"It's not something we like and we're looking at what we can do.
"It doesn't look pretty when you get the tread going away like that and we are looking at it and seeing if there are things we can do to eliminate it."
"It's a concern if the tyres fail," said Di Resta "but I'm not going to comment because we don't know what happened. We're a team that's light on tyres. We'll see what Pirelli come up with. No other car's had it today so maybe we were a bit unlucky."
In Bahrain, Pirelli suffered three failures - one on Hamilton's car in practice and two on Felipe Massa's Ferrari.
Pirelli initially said all three were caused by punctures before Hembery said after the race that Hamilton's may not have been.
A spokeswoman said a subsequent investigation had established that it was not a structural failure and the company was unable to determine the exact cause.