A method of generating an effective address that modifies the specified address given in the instruction by the contents of a specified index register. The modification is usually that of addition of the contents of the index register to the specified address. The automatic modification of index-register contents results in an orderly progression of effective addresses being generated on successive executions of the instruction containing the reference to the index register. This progression is terminated when the index register reaches a value that has been specified in an index-register handling instruction.