Sure, here's a Java program that converts string variables to double:

public class StringToDoubleConverter {
    public static void main(String[] args) {
        String str1 = "3.14159";
        String str2 = "2.71828";
        
        double double1 = Double.parseDouble(str1);
        double double2 = Double.parseDouble(str2);
        
        System.out.println("double1: " + double1);
        System.out.println("double2: " + double2);
    }
}

In this program, we first create two string variables: str1 and str2.

We then use the Double.parseDouble method to convert the strings to double values. This method takes a string as input and returns the equivalent double value.

Finally, we print out the double values of double1 and double2 to confirm that the conversion was successful.

Note that if the input string is not a valid double value (e.g. "hello" or "3.14.159"), the Double.parseDouble method will throw a NumberFormatException. It's important to handle this exception in your code if there's a possibility that the input string might not be a valid double value.