In the process of trouble shouting a mud disposal system, I found that although the discharge point has an elevation below the suction point; thus giving a negative static head, there is a hill in between wich is 100 ft above suction elevation. How could I take in account that hill in the system determination ?

The pump needs to be able to develop 100ft head so as to pump to the elevation of the highest point, ie round 100ft. Once the pump is primed,running and the discharge line is full to the highest point and flow is established over the high point a syphon effect may then come into play, this will then change the total head on the pump and introduce a new set of operatinmg conditions.
  
This has been discussed here before and maybe someone wiill be able to give you a lead into the right area so you can review it.

One should draw a diagram for the system. In the best case, once the line is filled the lowest pressure that could be achieved at the top of the hill is zero PSIA. That would be equivalent to 33.9 ft of water at 4C at sea level. Since it appears that you have a heavier fluid the head in feet of fluid would be proportionately lower.
If the circumstances permit one could prime the system with water and then start with the heavier fluid.

Since your fluid will have a vapour pressure the lowest pressure at the top will be the vapour pressure of your fluid.

Without knowing the details of the mud properties and the system configuration, it's a bit hard to tell if this is a hard project or not.
If the down hill pipe is relatively long and flat (especially the last part), hopefully the chance of slack flow is not high. With a pinch valve, throttling or shut close is not a problem. Hopefully the mud does not contain too much large particles so that wearing is not a big deal.

A startup proceure should includes pre-fill of all the piping (air pockets vent out), the pump will run close to design flow at the beginning of the operation and syphoning will be there most probably.

If THERE IS chance for a slack flow due to steep down slope, pinch valve(s) or orifice station should be considered. Be very careful about cavitation. Maintenance for "MUD" flow shall be OK.

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