When do I claim business travel expenses incurred in 2017 but reimbursed in 2018 and reported on 1099?

If you are self employed and entering this on a Sch C then the income is reported in the year you receive it and the expenses deducted in the year you paid them even if these things happened in different tax years. 

Thank you.  So the expenses I incurred in 2017 and received reimbursement in 2017 but is not reported on the 1009, I do not report, correct?

You report all income of any kind received in 2018 on the 2018 return even if you get no 1099 form for it.

Will do - thanks