HOUSTON (AP) _ Compaq Computer Corp. said today its earnings plunged 81 percent in the second quarter because of sluggish economies in the United States and Europe and a competitive personal-computer market.

Without an improvement in sales and economic conditions, Compaq President Rod Canion said the third quarter would be even worse.

For the second quarter, Compaq's net earnings amounted to $20.3 million, or 23 cents a share, down from $104.3 million, or $1.18 a share, a year ago.

Revenue fell 17 percent to $717.84 million in the quarter from $862.16 million a year ago.

In May, predictions of grim second-quarter earnings caused Compaq's stock to plummet 27 percent to $36 a share from $49.25 in one day. The company had predicted a 15 percent drop in profits for the quarter that ended June 30.

Compaq's stock closed Tuesday on the New York Stock Exchange at $32.12 a share.

Compaq began cutting prices on its personal computers in April, reducing suggested retail prices generally by one-third, but up to 68 percent on certain options. On Monday, it reduced by 22 percent prices on its notebook- sized personal computers.

''The U.S. economy continues to be weak and the industry-standard PC market remains sluggish,'' Canion said in a prepared statement. He also blamed poor performance on a soft market for personal computers in Europe as well as the consolidation of eight of the company's top 10 American dealers, which slowed reordering of Compaq products.

''This, combined with the economic and market conditions, plus significant price reductions, resulted in substantially lower unit sales and revenues,'' he said. ''A continuation of these trends, together with any greater strength of the U.S. dollar and the typical seasonal softness in Europe in the third quarter, would cause third-quarter results to be less than those for second quarter.''

Canion said the company also decreased operating expenses in the second quarter and would continue to reduce costs.

For the first six months, Compaq earned $134.6 million, or $1.49 a share, down 31.5 percent from $196.5 million, or $2.25 a share, a year ago.

Revenue fell 2.3 percent to $1.69 billion from $1.73 billion a year ago.