The FTSE 100 in London, Dax in Frankfurt and Cac 40 in Paris have fallen every day this week so far.
Shares are being hit by the rising yield on US 10-year Treasury bonds, which increases the returns that investors can make without risk.
Bond yields have grown because a rate cut in the US has become less likely.
Many traders see the US 10-year Treasury bond as the basic cost of capital, which means that any other investment must be compared with the return that could be made from Treasuries without taking any risks.
Less risk, more reward
At the end of February, the yield on the bonds was 4.5% and now stands at 5.16%, although it went as high as 5.25% earlier in the day.
That means that investors are less likely to invest in shares, because their return compared with a no-risk investment has deteriorated.
"Either you can take the same amount of risk for comparatively less reward or you can take a lot less risk for more reward," said David Bloom, global strategist at HSBC.
The yield is the percentage return you receive when you invest in something.
Bonds provide fixed returns, which means that when their prices go down, the yield goes up.
Treasury bond prices go down if interest rates are going up.
Last week's minutes from the Federal Reserve's rate-setting meeting said that inflation was still the "predominant concern" for the economy.
This has been taken to mean that interest rates will not be cut in the near future, so Treasury bond prices have declined.
Then on Tuesday, Federal Reserve chairman Ben Bernanke predicted that the US economy would rebound, even though housing sales are still falling.
Less attractive
The crisis in the US housing market has been the big threat to the US economy, so the perception that it might have weathered the storm has also put downward pressure on bond prices and increased yields.
With shares now a less attractive investment, stock markets in Europe and the US have had a bad week.
But the yield on Treasury bonds fell in early trading in the US, so Wall Street shares opened higher and European shares have recovered some of their earlier losses.
The FTSE 100 ended last week at 6,676.7, its highest close since September 2000.
By mid-afternoon on Friday, it had fallen to 6,488.1, which is a fall of 2.8% for the week.
Frankfurt's Dax started the week at 7,987.85, having gained almost 250 points in the week.
This week it has fared less well, trading at 7,602.39 on Friday morning, which is a fall of 4.8% in the week so far.
In Paris, the Cac 40 flitted between positive and negative territory on Friday.
By mid-afternoon, it was up 20.74 points at 5911.23, but it but later fell back to 5848.91, which is 4.2% lower than the 6,168.15 at which it started the week.