Tropical Storm Harvey was named at 5PM Thursday, as Hurricane Hunter aircraft flew into the storm and found maximum sustained wind of 40 MPH, with higher gusts.
The storm at 5PM Thursday was located about 355 miles to the east of St Lucia and moving to the west at 18 MPH.
The National Hurricane Centre says slow strengthening is possible during the next 48 hours.
Tropical-storm-force winds extend outward up to 35 miles (55 km) to the north of the centre.
This path will take the storm through the Caribbean Sea through the upcoming weekend and early next week.
Tropical Storm Warnings are in effect for St, Lucia, Martinique, Barbados and St. Vincent and the Grenadines.
A Tropical Storm Watch is in effect for Dominica.
Forecasters say Harvey is expected to produce rainfall totals of 2 to 4 inches across portions of the Windward Islands from Martinique southward to Grenada.
These rains could cause life-threatening flash floods and mudslides, according to the National Hurricane Centre.