Considering that no one could help on this case, as usually I solved this by myself. Here is the solution (in this example StartRow, StartCol, and HowMany variables' values are set in advance, I don't give their value in this case):
shtName = "Aug12"
Cr = "Criteria1"
Cr2 = "Criteria2"
with ThisWorkbook.worksheets(shtName)
Rng1 = .Range("A1").Offset(StartRow - 1, StartCol1 - 1).Resize(HowMany, 1).AddressLocal
Rng2 = .Range("A1").Offset(StartRow - 1, StartCol2 - 1).Resize(HowMany, 1).AddressLocal
Rng3 = .Range("A1").Offset(StartRow - 1, StartCol3 - 1).Resize(HowMany, 1).AddressLocal
Sum = Application.Evaluate("=SUMPRODUCT(('" & shtName & "'!" & Rng1 & "=" & Chr(34) & Cr & Chr(34) & ")*('" & shtName & "'!" & Rng2 & "=" & Chr(34) & Cr2 & Chr(34) & ")*('" & shtName & "'!" & Rng3 & "))")
end with
Important thing to consider: if in chosen range Rng3 are any non numeric values, then evaluate formula returns an error. In my case there were column names in the first row, so I needed to include StartRow variable, which is equal to the next row number below column names row (so that only numeric values would be included in a range).
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