There were many forms of crucifixion that the Romans employed - from the simple upright pole, actual trees, varying positions of the crossbars, or even multiple poles.
However, information found in scripture and history narrow the possibilities and predominantly give evidence towards Christ's cross being one with both a vertical pole (stipes) and crossbeam (patibulum) in the form of a low tau/lowercase t.
First, Jesus was ordered to 'carry his own cross. (John 19:17, Matt 27:32). This would not have been the entire cross that he carried, as is often portrayed in film and media, but rather the crossbeam of his own cross (the patibulum). A full cross would have weighed over 300lbs. The vertical portion of the cross, the stipes, was permanently fixed in the ground. History never records a case of a prisoner carrying the stipes. The Romans often had someone condemned carry the crossbeam, the patibulim, to add to their humiliation and punishment. Once the entire cross was set up, the condemned being lifted up in to position, they would leave the cross with it's new crossbeam up for future crucifixions.
See the Structure of the Cross for more details.
As the Romans did not have this practice of making the prisoner carry the patibulum for crucifixions on simple upright poles, nor had a known practice of making prisoners ever carry the vertical stipes, then the idea Christ might have been crucified on a simple pole goes against scripture and custom in this instance.
Scripture also gives the clue that Jesus was 'lifted up' (John 3:14) Jesus would have literally been "lifted up" in the method of crucifixion where a prisoner carried the crossbeam, as he would have either been attached to the patibulum and lifted to the stipes, or attached to the cross entire and lifted up.
Another clue scripture gives is the description of "nails", in the plural, through his wrists. (John 20:25) This would not have been the practice of crucifixion involving a single upright pole, as with a single pole the practice was to only use one nail.
One piece of scripture, that Pilate had a notice prepared and fastened to the cross declaring Christ the King of the Jews, does not give a direct clue about the shape of the cross. The 'titulus', a plaque written with gypsum letters on a board bearing notice of the condemned's name and crimes, was carried by a soldier during the processional where the condemned carried the patibulum and later fastened to the cross. This titulus crucis could have been placed on almost any shape of cross besides an X: a 'high tau' or 'low tau' cross - that is a cross like a capital case T or a cross like a lower case t, or a single pole could have all carried this sign equally well.
Moving on from scripture to history, Iraneus mentions the five extremities of the cross:
"The very form of the cross, too, has five extremities, two in length, two in breadth, and one in the middle, on which [last] the person rests who is fixed by the nails." Iraeneus, 'Against Heresies', Book II, Chapter 24 (175-185 AD)
On their own, a low tau cross has four extremities, a high tau cross only three, and a pole only two.
Yet this is easily explained by another piece found frequently in Roman crucifixions, the sedile. The sedile was a small seat or protrusion about halfway down the cross. It was not there for comfort, but to prolong agony by preventing early asphyxiation.
With the addition of a sedile, the low tau cross has five extremities.
Justin Martyr (100-165 AD) gave a vivid idea of the form of the cross in his comparison of the cross to a spitted, roast lamb,
"That lamb which was commanded to be wholly roasted was a symbol of
the suffering of the cross which Christ would undergo. For the lamb,
which is roasted, is roasted and dressed up in the form of the cross.
For one spit is transfixed right through from the lower parts up to
the head, and one across the back, to which are attached the legs of
Considering these clues in history and scripture, Jesus very likely died on a cross with a proper crossbeam. From scripture alone it cannot be divined the exact form of the cross, but Roman customs regarding crucifixion narrow the possibilities down. From at least the second century church tradition was already holding to the little t cross, which doesn't make it automatically a true reflection of history, but is another point in favor of the little tau, 't' cross.