I work at a cemetery in Texas and we have a monument business also, last week two co-workers and I were sent out of town for a training in monument designing.. we flew from home on a Thursday and came back on Sunday.. I was told that we were just going to be paid for Thursday and Friday.. but not for saturday when in fact we were still in a training session.. Is this right? or should we get paid for the hours that we were on training on saturday?.. Thanks for any info regarding this... I get paid on an hourly basis...

If the training was mandatory, you must be paid for the time, no matter on what day it occurs. I'm assuming, of course, that you are a nonexempt (generally speaking, hourly-paid) employee. If you are exempt, no additional pay is required.
http://www.dol.gov/dol/allcfr/ESA/Title_29/Part_785/29CFR785.27.htm
http://www.dol.gov/dol/allcfr/ESA/Title_29/Part_785/29CFR785.28.htm

And you didn't specifically ask this, but the flying time on Sunday is also compensable, assuming it occurred during your regularly scheduled work hours (excluding meal period, if applicable), even though you may not normally work on Sundays.
http://www.dol.gov/dol/allcfr/ESA/Title_29/Part_785/29CFR785.39.htm

just checking if I undestood correctly the articles you enlisted on your reply:

according to this, hours are not counted as working time if in fact they never led me to believe that not going to this training would mean that it would adversely affect my employment, which meant that i was going voluntarily.. and about the travel time on Sunday.. it's a little confusing.. because of the last paragraph which reads:

"As an enforcement policy the Divisions will not consider as worktime that time spent in travel away from home outside of regular working hours as a passenger on an airplane, train, boat, bus, or automobile"... does this mean that for me to get paid that travel time.. I would have to be the driver of the means of transport used to get to where the training would take place?..

sorry for all the questions I just want to be well informed and have a solid background when i talk to my supervisor.. and Thank you in advance for your help

The hours of Sunday that would be "eligible" for compensation would be those same hours you work on your normal workshift. Let's say your normal shift is 9 to 5. If your travel arrangements occur outside that window; then none of your travel would be compensable. Also your time in-flight as a passenger would not be compensable. I hope this clears it up for you.

just checking if I undestood correctly the articles you enlisted on your reply:

according to this, hours are not counted as working time if in fact they never led me to believe that not going to this training would mean that it would adversely affect my employment, which meant that i was going voluntarily.. and about the travel time on Sunday.. it's a little confusing.. because of the last paragraph which reads:

"As an enforcement policy the Divisions will not consider as worktime that time spent in travel away from home outside of regular working hours as a passenger on an airplane, train, boat, bus, or automobile"... does this mean that for me to get paid that travel time.. I would have to be the driver of the means of transport used to get to where the training would take place?..

sorry for all the questions I just want to be well informed and have a solid background when i talk to my supervisor.. and Thank you in advance for your help

Robb71 has given you the correct answer on the travel. And you are correct that in order to be paid for ALL your travel time on Sunday (not just the flying time, you would have had to take your own personal vehicle at the company's request.

Regarding the training, you read the regulation wrong. The first link says that all four of those conditions must be true in order to consider the training time noncompensable. If any ONE of them is NOT true, then the time must be paid. Since the training was mandatory, #1 is not true, and the time is therefore considered working hours.

Thank you very much for the explanation, i got it now... so the flyíng time not compensable is if it occurs outside my work hours..in my case (8 to 5)..and also understand about the 4 conditions to make the time non-compensable I appreciate your responses and I also apologize for not answering earlier, but I was able to log in until now.. thanks again Pattymd and robb71 for your help..