Most likely, a nonresident alien who files a Form 1040 instead of a Form 1040NR will pay too little tax. This is because the Form 1040 allows an individual to claim certain tax deductions that are usually not allowed for nonresident aliens (for example, standard deduction, medical deduction).A nonresident alien who filed a Form 1040 instead of a Form 1040NR should look into filing an amended return. See a tax professional for more information.