Albert Barnes Commentary Matthew 16:24

"Then said Jesus unto his disciples, If any man would come after me, let him deny himself, and take up his cross, and follow me." — Matthew 16:24 (ASV)

Let him deny himself. That is, let him surrender to God his will, affections, body, and soul. Let him not seek his own happiness as the supreme object, but be willing to renounce all, and lay down his life also, if required.

Take up his cross. See Barnes, Matthew 10:38.