It is not a bad idea to add in some supplemental weight training when training for these programs, as log PT is painful and can be very painful if your team is not working together under that log.  Prior to BUDS, I did a lot of military press - BUT not heavy - just lots of reps to build endurance/ muscle stamina.  A log may weigh 200 lbs but when you have 8 people under it you only lift 25 lbs or so many times.  Grabbing a set of 15-25 lb dumbbells and lifting overhead presses will work fine.  There are many other options too:

You can use a barbell for overhead presses or grab a partner and each of you hold one end of a barbell and press it together with 50-75lbs on it so you start to understand that this exercise is ALL about teamwork.  I also like these MJDB Workouts to mix in several exercises into one movement. 

There is a way to do overhead or push presses with a log by yourself as often many of us lack a buddy who wants to do these type of workouts.  See the Winter Workout video from my Youtube channel

Push presses are a good exercise to learn how to use the legs when doing these over head presses.  If you notice in the video it helps to get the legs involved in these lifts over head.

Many students will devote way too much time of their preparation months lifting weights daily.  To be honest, I never once wished I had lifted more weights while I was at BUDS.  But there were many days I wished I had run more to prepare for the daily mileage of timed runs, beach runs, and chow runs.

Log PT is painful. So are the boat carries.  But you are graded daily on runs, swims, obstacle courses, PT performance on the grinder.  These events will beat you down and get you boarded out of BUDS if you are not prepared for the stamina / endurance of training.  Any event at BUDS or other special ops training can get you kicked out if you are completely bagging it and not putting out as a team member, so being prepare for everything is smart.  Over-preparing for something that only occurs first phase (prior / during Hellweek) is not necessary.  Focus more on your graded events in the pool, runs on the beach and mixing in obstacle simulation training like this workout:

8 Count Pullups - This is a great way to simulate the runs in between a pulling / pushing event of obstacles.

As a former power-lifting football player, it was tough to give up weights to train for BUDS, but I was more than prepared physically for the log PT, boat carries, and other heavy laboring events.  See when it is most important to add extra weights to your 1-2 year preparation routine prior to Special Ops training in the article below:

Spec Ops Prep - the answer is IT DEPENDS on your athletic background if you really need to train with weights.  Some people need it - some do not.

If you have any questions, please feel free to email me at stew@stewsmith.com.  Your emails like this one helps me create articles each week.