With sqlserver 2005 and later you can use regex-like character classes with LIKE operator. See here.
To check if a string is a non-negative integer (it is a sequence of decimal digits) you can test that it doesn't contain other characters.
SELECT numstr
FROM table
WHERE numstr NOT LIKE '%[^0-9]%'
Note1: This will return empty strings too.
Note2: Using LIKE '%[0-9]%'
will return any string that contains at least a digit.
See fiddle