AN SF34 CREW TAXIED PAST THE HOLD LINE DURING TAXI FOR TKOF.

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EVENT: RWY INCURSION OF RWY 23L AT CLE ON DEC/XA/00. ON DEC/XA/00; I WAS OPERATING AS PIC IN A SCHEDULED COMMUTER OUT OF CLEVELAND; OH. I AM A CHK AIRMAN FOR THIS COMMUTER OPERATOR AND TODAY WAS THE LAST DAY OF A 2 DAY TRIP AND 6 DAYS (NOT CONSECUTIVE) OF IOE. THE STUDENT I WAS WITH WAS A CAPT UPGRADE; WITH 1000 HRS AS R SEAT PLT IN THIS SAAB 340A. THE STUDENT HAD BEEN DOING RATHER WELL UP TO THIS POINT; WHEN DURING OUR TAXI CHKLIST THE ACFT CROSSED THE HOLD SHORT LINE OF RWY 23L. THE STUDENT ADMITTED TO UNDERSTANDING THE CLRNC AND MY READBACK OF THE SAME; BUT IN PERFORMING A CERTAIN PART OF THE TAXI CHK; BOTH CAPT'S AND FO'S ATTN NEEDED TO BE DIVERTED FROM THE EXTERIOR OF THE AIRPLANE TO INTERIOR INSTS MOMENTARILY. AS I LOOKED UP TO CHK PROGRESS OF TAXI; I NOTICED THE FRONT OF THE ACFT HAD CROSSED THE HOLD SHORT LINE. BRAKES WERE APPLIED IMMEDIATELY AND THE ACFT RESTED 1/2 WAY ACROSS THE HOLD LINE. NO ACTION WAS TAKEN TO TAXI CLR OF HOLD LINE AS ACFT WERE BEHIND US. AS THE CHK AIRMAN AND PIC OF THE ACFT; I FEEL AS THOUGH I SHOULD HAVE PAID EXTRA CLOSE ATTN TO MY STUDENT'S TAXI PROGRESS AS WE NEARED THE HOLD SHORT LINE; AND NOT TAKE FOR GRANTED THE STUDENT'S PRIOR ABILITIES AND DEMONSTRATION OF COMMAND. A SECOND FACTOR WOULD BE THE TIMING OF THE PARTICULAR ENG TEST FUNCTION THAT REQUIRED BOTH OF OUR ATTN INSIDE THE COCKPIT. IN RETROSPECT; I WOULD HAVE LIKED TO BE STOPPED TO PERFORM THIS FUNCTION OF OUR TAXI CHKLIST. THE THIRD AND FINAL FACTOR WOULD BE THE CONFUSION WITH AN UNFAMILIAR ARPT THAT I SENSED FROM MY STUDENT. ALTHOUGH WE HAD BEEN TO CLEVELAND 2 OTHER OCCASIONS DURING OUR IOE TRAINING; THIS DAY WAS PARTICULARLY BUSY TO A SOMEWHAT CONFUSING INTXN OF RWYS AT CLE. OUR CLRNC WAS TO TAXI FROM THE TERMINAL TO RWY 23R; VIA TXWY U AND RWY 28; HOLD SHORT RWY 23L. I READ THIS CLRNC TO THE STUDENT. HE READ IT BACK TO ME AND SEEMED TO UNDERSTAND UNTIL HE HELD SHORT OF RWY 28. I EXPLAINED THE CLRNC AGAIN AND THE COURSE TO BE TAKEN; BUT HE STILL SEEMED SOMEWHAT APPREHENSIVE AMIDST THE EARLY MORNING RUSH OF TFC. FROM THERE; WE TAXIED DOWN RWY 28 BUT MISSED THE HOLD LINE DRAWN ON RWY 28 WHILE PERFORMING OUR CHKLIST.