I want to the same thing in tcl as the following C code:

#define VAL_A 1
#define VAL_B 2
#define VAL_C 4

int x = VAL_A|VAL_C;

switch (x & (VAL_A|VAL_C)) {
    case VAL_A: ... break;
    case VAL_A|VAL_C: break;

switch -regexp expr( x & VAL_A|VAL_C) \
     $VAL_A { } \
     $VAL_C|$VAL_C {} \

but that did not work.

I think the usage on vars as const is wrong at first. But are there
named constants in tcl???
The second is that I could not avaluate expressions as case value...

Any hint?

   switch -exact -- [expr {$x & ($VAL_A|$VAL_C)}] \
         $VAL_A                 { ... } \
         [expr {$VAL_A|$VAL_C}] { ... }

The next level of thought is to disconnect from representing things as
integers in the first place and instead look at other representations
that take advantage of the fact that strings are *the* fundamental
datatype of Tcl (by contrast, in C it's really the machine-word). That's
quite a change though, and probably requires a lot of reworking of the
rest of your program too.

    switch -- $something {
       FOO {
       }
       BAR {
       }
    }

is fairly close to the C:

    #define FOO 1
    #define BAR 2

    switch (something) {
    case FOO:
       break;
    case BAR:
       break;
    }

I re-remembered this recently writing some Tcl to parse 802.1D BPDUs:

    ...
    binary scan $bpdu "S c c c a*" \
        a(protocol) a(rstpVersion) a(type) a(flags) bpdu

    if {$a(protocol) != 0 } {
        error "Invalid protocol"
    }
    switch -- $a(type) {
        0 {
            set a(type) "CFG"
        }
        0x80 {
            set a(type) "TCN"
        }
        2 {
            set a(type) "RST"
        }
        default {
            error "Unknown BPDU type"
        }
    }
    ...

What should that "$VAL_C|$VAL_C" mean?

Even the original
     case VAL_A: ... break;
     case VAL_A|VAL_C: break;
does not make much sense in that order (VAL_A will always trigger in
the first clause, the second will never run).

The "|" in C-case is best thought of as the
   foo -
   bar { }
in TCL-switch, so try
  switch -- [expr {$x & ($VAL_A|$VAL_C)}] \
        $VAL_A { puts VAL-A } \
        SVAL_B - \
        $VAL_C { puts "VAL-B (will never trigger) | VAL-C" }

Note: the precedence of & and | in TCl-expr are the same as in C, so
you need the same grouping in TCL-expr as in C-switch.

    array set my_lookup_table {0    CFG
                               0x80 TCN
                               2    RST}
    set a(type) $my_lookup_table($a(type))

along with a bit of exception-handling.