It depends on what you are testing but the answer is essentially no, there is no current replacement for animals. Cell culture does not represent the workings of an organism well as they do not create interacting 3d, representative models. However there is a drive to improve our ability to grow human tissues and organs in vitro
for testing but we are a long way from being able to do that.
Whenever someone mentions in silico
I cringe at their lack of understanding. We can't even simulate how proteins fold with much accuracy or speed, to simulate the entire human body (you would need to do it atom by atom) would require computing power far in excess of anything of our wildest dreams. A bigger problem of that is that any computer simulation that realistic would be able to feel pain, have emotions and thoughts. You've moved the ethical problem from in vivo organisms to in silico